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haGat Delhi & Noida! Display replies flat, with oldest first Permutation and Combination by T o ta l Ga dha - Sunda y, 17 August 2008, 11:13 AM

Dagny has been telling me smugly that it's now my turn to write an article. So I decided to write one as soon as possible and pass the buck back to her. We both know that it takes a lot of pain to research for an article and write the text so we both try to avoid it for as long as possible. On the other hand, since we both enjoy writing and like to publish a well-finished chapter, we both undertake the task eagerly once the ball is in our court. Writing these chapters have made me realize how true is the maxim "if you want to learn something well, teach it." I can cite a lot of topics which I learnt while teaching in the class or answering students' questions. These years of teaching have made so many topics seem pretty childish to me which were nightmares to me before. But knowing a topic well and teaching it are two different ball games. Many a times, I have found myself struggling in the class to make a student understand something which I have found obvious to understand! The fault is not on the student's part. Three or four years ago, I would have been stuck on the same point! Every time I encounter a situation like this, my only measure is to stop at that point, retrace my steps with the students and slowly unravel the difficulty he's facing. It works most of the times. But sometimes, the student is in so much awe with the topic that his mind gets frozen. I have seen this happening many a times. Topics such as time, speed and distance, Permutation and C ombination, geometry etc. inspire so much fear among the students that sometimes simple principles, which they would have otherwise understood do not strike them as simple. I get incessant queries such as "Sir, time speed distance chhod sakte hain?," "Sir, permutation combination na karein to chalega?" from my students all the time. And the sad part is, that the level of C AT in these topics is very simple. They are doable. In the present chapter, I am trying to present one of these dreaded chapters as I understand it. I hope my students understand it too.

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I shall have to end here and leave the rest of it for my CBT Club students. I shall c over some problems based on this in the CBT Club this week.

If you think this article was useful, help others by sharing it with your friends!

You might also like: Probability Maxima, Minima and Inequalities R eply

Re: Permutation and Combination by va m si k rishna - Sunda y, 17 August 2008, 12:23 P M

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Tatz a GEM OF AN ARTICLE thnk z,

VaMsI S how parent | R eply

Re: Permutation and Combination by Am it A - Sunda y, 17 August 2008, 05:22 P M Now what do i say other than "T HANKS A LOT T G !!! " u rock

....

Amit S how parent | R eply

Re: Permutation and Combination by Am it Kum a r - Sunda y, 17 August 2008, 06:14 P M Ve ry Ve ry use ful a rticle .. T ha nk s S how parent | R eply

Re: Permutation and Combination by Le o nida s S - Sunda y, 17 August 2008, 06:20 P M Hi T G, A fa bulo us a rticle .I think the re is a m ista k e in the so lutio n o f P ro b 3 o f the 4 frie nds pro ble m . It sa ys "T he to ta l num be r o f wa ys in which 4 frie nds ca n sta y to ge the r is 104

" I think it sho uld be 10000 a s yo u fo und o ut e a rlie r. S how parent | R eply

Re: Permutation and Combination by Am it Kum a r - Sunda y, 17 August 2008, 09:40 P M Hi T G, Answe r to 'Go o d Bo y Ba d Bo y' m o vie que stio n: Since the se two co uple s wa nt to sit to ge the r a t e ithe r e nd. No w, we 'll tie the m to ge the r. He nce , to ta l num be r o f stude nts will be 7 o ut o f which 6 stude nts ca n sit in 6x 5x 4x 3x 2x 1 = 720 wa ys. a nd the co uple ca n sit a t e ithe r e nds (i.e 2 wa ys) a nd the co uple s ca n sit in 2 wa ys a m o ng the m se lve s a nd fina lly, in e a ch co uple , bo y a nd girl ca n sit in 2 wa ys(BG a nd GB)(T o ta l = 2x 2 wa ys). He nce , Num be r o f wa ys a ll ca n sit will be : 720x 2x 2x 2x 2 = 11520 (Answe r) S how parent | R eply

Re: Permutation and Combination by Ma nik a T a ndo n - Sunda y, 17 August 2008, 10:41 P M he y T G... a we so m e pie ce o f writing dude ... ra the r tha nx da gny fo r giving him a push to write it... :D bo th o f u a ll ro ck .. che e rs,

S how parent | R eply

Re: Permutation and Combination by AsHwIn Drm z - Sunda y, 17 August 2008, 11:02 P M hi....T g....

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions G8 a rticle ...thk u so m uch fo r a wo nde rful a rticle ,a ctua lly i wa s wo rrie d a s u we re no t writing a rticle s fo r ca t 08 stude nts....but nw m so gla d a nd co nfide nt da t m y a ll wo rrie s will va nish.T g ca n u plz write a n a rticle o n pro ba bility to o .... S how parent | R eply

Re: Permutation and Combination by Ashwin A - Mo nda y, 18 August 2008, 07:51 AM T G Sir! Sim ply Fa nta bulo us!! Just wa nte d to k no w do u ha ve a Bo o k ha ving a ll to pics o f Q ua nt...I ha ve the bo o k o n Num be r the o ry which in itse lf,

is ve ry go o d.!!! S how parent | R eply

Re: Permutation and Combination by Da gny T a gga rt - Mo nda y, 18 August 2008, 09:17 AM He y Ma nik a , T G pla ye d sm a rt this tim e . I a sk e d him to write a n a rticle thre e da ys ba ck ;he wro te , e dite d a nd uplo a de d it within two da ys. No w the ba ll is

ba ck in m y co urt. S how parent | R eply

Re: Permutation and Combination by Diwa k a r Bha sk a r - Mo nda y, 18 August 2008, 09:47 AM T hnk s a lo t T G........... i do nt ha ve wo rd to sa y a nything m o re ................... S how parent | R eply

Re: Permutation and Combination by va m si k rishna - Mo nda y, 18 August 2008, 11:13 AM He y Am it, P l R e che ck Shudn't Ans be 720 x 2 x 2 x 2 1..six stude nts ca n be a rra nge d in 6! = 720 2..T he 2 co uple s ca n sit a t e ithe r o f the e nds in 2 wa ys 3..a nd the n e a ch co uple o n e ithe r side ca n e x cha nge the ir se a ts..in 2 wa ys so two co uple s ca n do ta t in 2 X 2 wa ys re ga rds, Va MsI S how parent | R eply

Re: Permutation and Combination by Krusha ng Sha h - Mo nda y, 18 August 2008, 11:36 AM

T HANKS A LO T

TG!!!

its a wo nde rful a rticle ..... S how parent | R eply

Re: Permutation and Combination by a m it k um a r - Mo nda y, 18 August 2008, 01:44 P M T ha nk s T G Awe so m e Article ....... S how parent | R eply

Re: Permutation and Combination by nik hil k ha nde lwa l - Mo nda y, 18 August 2008, 04:58 P M T ha nk s a lo t T G Do ing a gre a t jo b

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Re: Permutation and Combination by ra jde e p cho udhuri - Mo nda y, 18 August 2008, 05:46 P M Hi T G, T he a rticle is sim ply m ind blo wing!!!P lzzzzzzzz po st a n e x e rcise o n P e rm uta tio n a nd C o m bina tio n pro ble m s. S how parent | R eply

Re: Permutation and Combination by brya n co le - T ue sda y, 19 August 2008, 12:59 AM Is the a nswe r to a +2b+3c.....to ta l num be r o f e le m e nts is 36? S how parent | R eply

Re: Permutation and Combination by T o ta l Ga dha - T ue sda y, 19 August 2008, 03:37 AM Hi R a jde e p, Abo ut the e x e rcise , ha ve yo u se e n the a rticle co m ple te ly? T o ta l Ga dha S how parent | R eply

Re: Permutation and Combination by ra jde e p cho udhuri - T ue sda y, 19 August 2008, 04:22 P M

Yes .But i fe e l it will be lo t m o re he lpful if yo u ca n give us a n e x e rcise lik e the o ne o n Num be r Syste m pro ble m s,I m e a n ple nty m o re pro ble m s to so lve .Also whe re ca n i ge t the a nswe rs to the se pro ble m s??? Anywys T G ro ck s!!!! S how parent | R eply

Re: Permutation and Combination by R iya z Iqba l - W e dne sda y, 20 August 2008, 11:03 P M Hi T G, Ex ce lle nt a rticle ,a s usua l.I've a que stio n a bo ut the 'co unting functio ns' pro ble m .T he no .o f functions fro m a 5-e le m e nt se t to 7-e le m e nt se t sho uld be le ss tha n 7^5,right? 7^5 sim ply re pre se nts the num be r o f ordered pairs (x ,y) fro m first se t to the se co nd.Se ve ra l o f the m m a y co rre spo nd to a single function.e g: (1,1) (2,2),...(5,5) a re five distinct o rde re d pa irs but a single functio n viz y=x . Am I m issing so m e thing? S how parent | R eply

Re: Permutation and Combination by a nds a nds - T hursda y, 21 August 2008, 07:22 AM a sh, hi I've just sta rte d with the Num syste m but a m finding the a re a va st,e no m o usly huge a nd the to pics no t co nce ntra te d fro m a pa rticula r so urce .Fro m yo ur po st I se e tha t the re is so m e co nso lida te d re so urce fo r the Num syste m yo u ta lk in a bo ut o r is the the e bo o k by T G ppl.C a n yo u po st o n the na m e he re .It wo uld be sure he lp if I a m to find the bo o k a nd the co nte nts sa tisfying.T ha nk s.....!!!! S how parent | R eply

Re: Permutation and Combination by T o ta l Ga dha - T hursda y, 21 August 2008, 01:18 P M Hi R iya z, T he re a re 7 5 a rra nge m e nts, a nd e ve ry a rra nge m e nt, m a pping 5 e le m e nts o f se t 1 to 7 e le m e nts o f se t 2 wo uld be co unte d a s a single functio n o nly. T o ta l Ga dha S how parent | R eply

Re: Permutation and Combination by Sha lini B - T hursda y, 21 August 2008, 02:45 P M Hi T G,

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions I ha ve re giste re d fo r yo ur C o pyca t e x a m s by pa ying thro ugh cre dit ca rd but I a m fa cing pro ble m s while trying to write the e x a m o nline . I ha ve m a ile d yo u lo ng ba ck a bo ut this (to the co pyca t e m a il ID a nd a lso to a dm in e m a il ID). But I ha ve no t re ce ive d a ny a nswe r fo r tha t. And I co uld no t find a ny co nta ct num be r to o o n this site whe re I co uld ca ll up a nd re po rt m y pro ble m . P le a se re spo nd. C o nte nt fro m m y pre vio us m a il da te d July 30th 2008 to yo u be lo w: My pro ble m is tha t whe n I trie d ta k ing co pyca t 2 the site wa s unre spo nsive a nd did no t na viga te to the ne x t pa ge a t a ll. I trie d ta k ing the e x a m but whe n I sta rte d with it a nd e nte re d m y o ptio ns fo r the first pa ge a nd click e d o n the Ne x t butto n, the site be ca m e ve ry slo w a nd did no t sho w the ne x t pa ge a t a ll. I trie d se ve ra l tim e s but it wa s o f no use . I che ck e d the bro wse r co m pa tibility te st a nd it sa id m y syste m is fine fo r ta k ing the te st a nd m y inte rne t co nne ctio n is go o d a nd a ll o the r we bsite s a re wo rk ing fine . I a m m ighty disa ppo inte d. P le a se lo o k into this pro ble m ASAP S how parent | R eply

Re: Permutation and Combination by m a no j 1123 - T hursda y, 21 August 2008, 04:06 P M Hi T G, T ho ugh I fe e l no t o k to write he re , I a m a lso fa cing the sa m e pro ble m , no t a ble to bro wse to ne x t pa ge . m a y be if the pa ge re m a ins o pe n fo r so m e tim e the co nne ctio n to ur se rve r bre a k s. P le a se se nd the pdf fo r the C O P Y C AT s to m y m a il be fo re ha nd. So tha t I ca n ta k e print a nd a ppe a r the te st.. P lz find a so lutio n fo r us. T ha nk s. S how parent | R eply

Re: Permutation and Combination by Le o nida s S - Frida y, 22 August 2008, 10:33 P M Hi T G,

T ha t wa s a n e x ce lle nt a rticle C a n yo u ple a se po st so m e a rticle s o n functions,logarithms and probability

S how parent | R eply

Re: Permutation and Combination by ra k e sh o jha - Sunda y, 24 August 2008, 08:02 P M hi de a r First o f a ll ..thnx a lo t fo r such a nice co lle ctio ns o f que stio ns which ha s he lpe d to build the funda m e nta ls o f this to pic...

i just ha ve o ne do ubt in o ne o f the e x a m ple s ..a bo ve whe re we a re ge tting num be r o f 7 didgit num be rs ...in bina ry.....tha t pa rt is o k ... but whe n the num be r is co nve rte d to de cim a l ba se ....the re will be o the r co nditio ns a prt fro m la st 3 digits a s ze ro s........sa y a bina ry no whe n co nve te d to de cim a l a nd be co m e s 24...tha t is divisble by 8.... m a y be i m wro ng so m e whe re but plz te ll m e why o nly yo u ha ve ta k e n the co nditio n o f la st 3 didgits a s 0 fo r dibisiblity by 8...why no t o the r co nditio ns....

thnx ra k e sh S how parent | R eply

Re: Permutation and Combination by T o ta l Ga dha - Sunda y, 24 August 2008, 10:12 P M Hi R a k e sh, C o nve rt 24 to bina ry ple a se ? T o ta l Ga dha S how parent | R eply

Re: Permutation and Combination by a m it k um a r - Mo nda y, 25 August 2008, 01:31 AM HI ALL, que stio n.>the re a re 10 stude nts o ut o f which thre e a re bo ys a nd se ve n a re girls,in ho w m a ny diffe re nt wa ys ca n the stude nts be pa ire d such tha t no pa ir co nsists o f two bo ys? Una ble to so lve this.P le a se he lp wid pro pe r e x pla na tio n S how parent | R eply

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions Re: Permutation and Combination by IR O NMAN A - Mo nda y, 25 August 2008, 11:57 AM

T ha nk s a m illio n

fo r the be a utiful a rticle T G.

I ha ve a sm a ll do ubt. P lz do e x pla in m e . "There are 6 tasks & 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned either to person 3 or person 4. Every person must be assigned one task. In how many ways can the assignment be done(CA T 2006)?" W ha t's the wro ng in m y pro ce dure .... First person: As ta sk 1 & ta sk 2 ca nno t be a ssigne d a ny o f the o the r 4 ta sk s ca n be a ssigne d to him - 4 ways Second Person: As ta sk 1 & ta sk 2 ca nno t be a ssigne d, a nd o ne a lre a dy a ssige nd to P e rso n 1, a ny o f the o the r 3 ta sk s ca n be a ssigne d to him - 3 ways Third Person & Fourth person: o ne o f the se ge t T a sk 2. T he o the r ge ts a ny o f the o the r 3. (o ne o f ta sk s 1,3,4,5,6 (le a ving the ta sk s a ssigne d to P e rso ns 1 & 2) - 3 ways Fourth & Fifth Persons: o the r 2 ta sk s ca n be a ssigne d in 2 ways. total = 4*3*3*2 = 72 P lz do a nswe r m e .. tha nk s in a dva nce S how parent | R eply

Re: Permutation and Combination by a rpi sin - Mo nda y, 25 August 2008, 12:20 P M T G/Da gny W o nde rful wo rk !!! I wa s go ing thro ugh the num be r syste m quiz,a nd ha ve a do ubt in a que stio n .W he re ca n I po st m y que ry ? R e ga rds Arpita S how parent | R eply

Re: Permutation and Combination by Sure ndra n C ha ndra va tha na n - Mo nda y, 25 August 2008, 09:43 P M Hi Am it, He re 's m y try... 1st A pproach 1 bo y ca n pa ir up wid 7 girls in 7 wa ys...So fo r 3 bo ys, to ta l no . o f wa ys is 21..And 1 girl ca n pa ir up wid 6 o the r girls in n(n-1)/2, ie , (7x 6)/2 = 21 wa ys..(o r) Just 7C 2 = 21 will ce de u the a nswe r. So the fina l a ns is 21 + 21 = 42 wa ys.. [[O R ]] 2nd A pproach Sho uld this pro ble m be so lve d lik e be lo w....??? T o se le ct 2 ppl fro m 10, we ca n do in 10C 2 = 45 wa ys..And a rra nging the m in pa irs ca n be do ne in 45x 2 = 90 wa ys..(o r) juz we ha ve to a rra nge 2 pla ce s o ut o f 10 which ca n be do ne in 10P 2 = 90 wa ys.. And the n, 3 bo ys ca n be pa ire d up in 6 wa ys.. So is the fina l a ns 90 - 6 = 84 wa ys ?????? I a m pe rple x e d.. Which ans is correct, TG ????? A ppreciate ur comments......... Be st R gds, Sure n S how parent | R eply

Re: Permutation and Combination by Sure ndra n C ha ndra va tha na n - Mo nda y, 25 August 2008, 09:58 P M T GGGGGG, Ur a rt o f so lving & sim plifying the pro ble m s le a ve s m e in a we but it invite s m o re co nfusio ns..... I wud sa y da t the be lo w pro ble m ca n be so lve d e a sily but u sa id it is no t so .. In how many ways can four persons be seated out of 5 boys and 3 girls on four different seats? No w se e , to ta lly thr a re 8 ppl whe re the y 've to be se a te d in 4 se a ts.. So wo n't the no rm a l pe rm uta tio n fo rm ula do ???????

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions ie , 8P 4 = 1680 wa ys.... P lz e lucida te the fa ct fo r bre a k ing the pro ble m & co nside ring 4 ca se s in ur a ppro a ch.... T ha nk s in a dva nce , Be st R gds, Sure n S how parent | R eply

Re: Permutation and Combination by Bla ck i - Mo nda y, 25 August 2008, 11:38 P M Hi T G, It is re ga rding the '7 digit binary no div. by 8 when converted to decimal no' que stio n. Ho w ca n o ne de cide tha t the la st 4 bits , if a re e qua l to ze ro the n the no is divisible by 8 whe n co nve rte d to de cim a l ? Suppo se the sa m e que stio n a sk s a bo ut o cta l no inste a d o f bina ry, ho w sho uld o ne de cide a bo ut it ? S how parent | R eply

Re: Permutation and Combination by a m it k um a r - T ue sda y, 26 August 2008, 10:21 P M Hi Answe r is 630.give a no the r try. S how parent | R eply

Re: Permutation and Combination by Ha rish Ba nsa l - T hursda y, 28 August 2008, 12:51 P M

Hi TG, Gr8 article.... Plz post the solutions of the problems that you have mentioned in ur artical... We want to match our answers and approach. And plz can u post something on probability prior to CAT 2008. Eagrly waiting for a reply.........

S how parent | R eply

Re: Permutation and Combination by T uhin Ba ne rje e - T ue sda y, 2 Se pte m be r 2008, 05:14 P M

Hi TG, it's realy a mind blowing article on permutation and combination. I have question on the same topic and have two different approaches , kindly tell me which one correct : Question: Ten students have been shortlisted to form two teams of six students each, such that there are exactly three common between the two teams, In how many ways can the teams be formed. Ans: 1st approach: Three common stuednts we can take out of 10 students = 10 C3 ways

,

We need to build each group having 6 students , for the 1stGR. rest of the 3 students we can take out of 7 students = 7C3 ways So , 1stGR complete, for the 2ndGR we can take rest of the 3 students out of the 4 students in = 4C3 ways. Total = 10 C3 * 7C3 * 4C3 = 16800

2nd Approach : From 10 students , 3 students commonbetween the two teams can be selected in = 10C3 ways. since 7 students are still left and for each team we need 6 students , Now select the student will find a place in neither team and it can be done in = 7C1 ways. http://totalgadha.com/mod/forum/discuss.php?d=3537

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Now remaining 6 students have to divided into two groups of 3 each and it can be done in = 6C3 / 2 Now two teams can be formed = 10C3 * 7C1 * 6C3 / 2 = 8400 please tell me where I am missing the concepts

S how parent | R eply

Re: Permutation and Combination by rudra sa m a l - T ue sda y, 2 Se pte m be r 2008, 10:01 P M Hi T G, In the e x a m ple whe re u a sk e d: Ho w m a ny a rra nge m e nts r de re o f six 0's, five 1's a nd fo ur 2's, whe re (i)first 0 pre ce de s first 1? shudnt the a ns be 343980 a nd no t 349380?.... a nd the re 's a n e a sie r wa y a s we ll. It go e s lik e this: to ta l a rra nge m e nts=(15!/(4!*5!*6!)) so a ns will be =to ta l a rra nge m e nts*(p/q) whe re q=a ll po ssibl a rrngm nts o f the 1s a nd 0s p=a rrngm nts whe re 0 o ccupie s 1st po sitio n so , q=11!/(6!*5!) p=10!/(5!*5!) a ns=343980

S how parent | R eply

Re: Permutation and Combination by T o ta l Ga dha - W e dne sda y, 3 Se pte m be r 2008, 10:49 AM Hi R udra , C o rre cte d the typing e rro r. And go o d wa y to so lve the que stio n. T o ta l Ga dha S how parent | R eply

Re: Permutation and Combination by T o ta l Ga dha - W e dne sda y, 3 Se pte m be r 2008, 10:51 AM Hi T uhin, T he se co nd so lutio n is co rre ct. First ha s re pe titio n. P le a se che ck the que stio n o f "thre e sta te s with thre e stude nts fro m e a ch sta te ...." T o ta l Ga dha S how parent | R eply

Re: Permutation and Combination by bha ge e ra th n - W e dne sda y, 3 Se pte m be r 2008, 10:30 P M hi i'm he re fo r the first tim e .. this wa s pre tty he lpful.. ho w do i cro ss che ck if i go t the right a nswe rs?? will the so lutio ns be a va ila ble fo r the que stio ns?? S how parent | R eply

Re: Permutation and Combination by bha ge e ra th n - W e dne sda y, 3 Se pte m be r 2008, 11:04 P M Hi T G, fo r the que stio n In ho w m a ny wa ys ca n fo ur pe rso ns be se a te d o ut o f five bo ys a nd thre e girls o n 4 diffe re nt se a ts? sho uld we ta k e tho se ca se s a s m e ntio ne d by yo u?? why ca nt we do it lik e this?

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions the re a re 8 pe o ple in a ll.. se le ct fo ur o f the m in 8c4 wa ys (70 wa ys). No w yo u ca n a rra nge the se fo ur in 4! wa ys(24 wa ys). So to ta l wa ys is 70*24 = 1680. is the re a nything wro ng with this a ppro a ch?? S how parent | R eply

Re: Permutation and Combination by Syd S - T hursda y, 4 Se pte m be r 2008, 01:58 P M k udo s fo r a no the r brillia ntly structure d a nd e dite d a rticle ,,,!!!! wa s just wo nde ring guys bo ut dis pro b,,, "in ho w m a ny diff wa ys ca n the fa ce s o f a cube be pa inte d in 6 diff co lo rs?" shudnt the no o f wa ys be 6 X 5 x 3!,, as the first face can be painted in 6 ways,, ra the r tha n o nly 1 wa y,, jus wa nte d 2 k nw,,y is it 5 X 3! ra the r tha n 6 X 5 x 3! thnx S how parent | R eply

Re: Permutation and Combination by brije sh go gia - Sa turda y, 6 Se pte m be r 2008, 07:12 P M T ha nk Y o u fo r this ve ry use ful a rticle . S how parent | R eply

Re: Permutation and Combination by ga ne sh p - Sunda y, 7 Se pte m be r 2008, 08:41 AM T ha t U Ve ry m uch sir

..........a s e x pe cte d m y se a rch fo r the be st a rticle o n pe rm uta tio n a nd co m bina tio n did e nd he re .. S how parent | R eply

Re: Permutation and Combination by k la da d a sda - Sunda y, 7 Se pte m be r 2008, 08:44 P M just be ing curio us. a re u va m se e k rishna fro m C SE IIT KGP , cla ss 2006??

If yo u a re k indly re ply ba ck , it wo uld be nice to k no w o ne m o re fa m ilia r fa ce a t T G S how parent | R eply

Re: Permutation and Combination by Ma nish Ka shya p - T ue sda y, 9 Se pte m be r 2008, 07:56 P M

Hi TG, My Solutions are 1)a 2)c 3)b 4) 5)c 6) 7)c 8)c 9)a 10)b 11)b 12)c 13)b 14)b http://totalgadha.com/mod/forum/discuss.php?d=3537

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15) 16) 17)b 19)d 20) 21)c 22)16725 23)24 24)840 25)120 26) 680 27)26!/2 28)45 29)21 30)35 31)5 32)7c 2 33)33600 I was not able to solve some questions for whic h I had not put any answers. Can you please verify my answers and tell me the solutions of whic h are wrong or whic h I was not able to solve. Thanks and Regards, Manish

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Re: Permutation and Combination by Ank it Aro ra - W e dne sda y, 10 Se pte m be r 2008, 05:27 P M Hi T G,

I ha ve n't so lve d a ll the que stio ns till no w...just wa nt to co nfirm the a nswe rs o f first 5 que s.. 1 (a ) 2(b) 3(d) 4. I m ge tting (26^3)*220 a s m y a nswe r 5(c)

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Re: Permutation and Combination by Ma nish Ka shya p - T hursda y, 11 Se pte m be r 2008, 03:09 P M Hi T G Sir, P le a se che ck the so lutio ns ple a zzzzzzzzzzzzzzz. I a m wa iting fo r so lutio ns. T ha nk s a nd R e ga rds, Ma nish S how parent | R eply

Re: Permutation and Combination by va m si k rishna - Frida y, 12 Se pte m be r 2008, 04:25 P M Frns

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Check/discuss answers for above problems @ http://totalgadha.com/mod/forum/discuss.php?d=3683 VaMsI S how parent | R eply

Re: Permutation and Combination by Sa ura bh She k ha r - Frida y, 26 Se pte m be r 2008, 09:59 AM Hi T G, C o uld yo u ple a se po st the co m ple te so lutio n to the Ex e rcise . W e a re a ll e a ge rly wa iting fo r it. Sa ura bh S how parent | R eply

Re: Permutation and Combination by Ve nk k a te sa n R - Sa turda y, 27 Se pte m be r 2008, 04:44 AM Hi sure n, I think the que stio n invo lve s just the se le ctio n. He nce the a rra nge m e nt is no t re quire d. He nce 10c2-3c2=45-3=42 is the a nswe r. S how parent | R eply

Re: Permutation and Combination by a rvind je na m a ni - Sa turda y, 4 O cto be r 2008, 09:19 P M Hi T G sir, T he link is fa bulo us. In co m bina tio n pa rt the re is a que stio n " In ho w m a ny wa ys 5 bo ys , 3 girls ca n be sitte d in 4 se a ts?" T he re we do n't ne e d to se gre ga te into pa rts lik e yo u m e ntio ne d. 8C 4 wa ys we ca n se le ct 4 pe o ple (witho ut co nside ring bo y,girl co m bina tio n) 4! wa ys to a rra nge the m . so , 8C 4*4!=8P 4=1680 which m a tch a lso yo ur a nswe r.

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Re: Permutation and Combination by Am it T rive di - Sa turda y, 11 O cto be r 2008, 10:31 P M

Hi TG sir, The lesson is really great. i have a doubt for one of the examples. the examplein whic h 5 boys and 5girls go to watc h the c inema spiderman3. you gave two arrangement for the wish of the boys "every boy wants to sit with a girl" and no two girls sit together i think other arrangement of the form are possible GBBGBGBGBG GBGBBGBGBG GBGBGBBGBG GBGBGBGBBG In the above arrangements every boy is sitting with a girl and no two girls are sitting together c larify my doubt, let me know where i am making mistake in reasoning. Warm Regards, Amit S how parent | R eply

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions Re: Permutation and Combination by Am it T rive di - Sa turda y, 11 O cto be r 2008, 11:57 P M if the co uple s a re siting a t the e nds the a ra nge m e nts a re 2 X 2 X 2 x 6! Am it S how parent | R eply

Re: Permutation and Combination by m e e na k - Sa turda y, 18 O cto be r 2008, 04:24 AM hi, for the states question can't we solve like this from 3states 3 students eachso selecting 5 frm 9= 9c5 then subtracting 6c5 (case where all 5 students are selected frm two states) ie:9c5 - 6c5 .pls tell me where the problm is

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Re: Permutation and Combination by no e l sa nde sh - Mo nda y, 3 No ve m be r 2008, 03:40 P M Hi T G, T his is in re ga rd to a n e x a m ple pro ble m (No . o f 7 digit bina ry num be rs tha t a re divisible by 8 whe n co nve rte d to ba se 10). i wa s wo nde ring a s to y the 3rd digit fro m the la st ca nno t be 1 o r 0. Y o u've m e ntio ne d tha t the la st 3 digits sho uld be 0. But if the la st 3 digits a re 100 the n its ba se 10 e quiva le nt will be 400 which is divisible by 8.... I'm re a lly ba d a t P n C but i ca n't figure o ut the lo gica l fla w in m y tho ught... C a n u he lp m e o ut o n this? S how parent | R eply

Re: Permutation and Combination by ra je sh k a m ba m pa ti - T hursda y, 6 No ve m be r 2008, 12:36 AM Y a i a gre e with yo u sa nde sh, i to o go t this do ubt.And i think we a re co rre ct. S how parent | R eply

Re: Permutation and Combination by T o ta l Ga dha - Frida y, 7 No ve m be r 2008, 12:49 AM (100) 2 = 4 (in de cim a l) S how parent | R eply

Re: Permutation and Combination by C o m ple te Ga dha - Frida y, 7 No ve m be r 2008, 08:03 P M Hi TG Sir, This is the best material i have ever come across for Permutation and Combination. I have been going through the material in the forum. all of them r so amazing that i am actually gaining the confidence to crack the CAT though i have not been doing so good in the mock cat. Thanks a lot..!! Hats off To U...!!! S how parent | R eply

Re: Permutation and Combination by Bhe e m e sh K - W e dne sda y, 12 No ve m be r 2008, 01:40 AM Hi T G, I ha d a do ubt in the first pro ble m (i.e 10 spe a k e rs pro ble m ) so lve d in the pe rm uta tio n se ctio n. I so lve d it in this m a nne r. yo u tie the P M, MP a nd MLA into a single pe rso n a nd the n ca lcula te the wa ys to a rra nge the m . wudn`t it be 8! the n tha t we ha ve o the r 7 spe a k e rs a nd 1 gro up o f P M, MP a nd MLA to a rra nge ? I find yo ur wa y a lso lo gica l but a m no t a ble to unde rsta nd diffe re nce be twe e n m y a ppro a ch a nd yo ur a ppro a ch. k indly ca n yo u e x pla in whe re I a m m issing the lo gic? S how parent | R eply

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions Re: Permutation and Combination by sum it ja m wa l - W e dne sda y, 4 Fe brua ry 2009, 08:51 AM

Hi T G,

I ha ve so m e pro ble m in unde rsta nding the co nce pt o f pa rtitio n pro ble m .. o f 5 ba lls a s sta te d be yo u. le t's ta k e * * * * * the se a s 5 sim ila r ba lls no w dividing the m into 3 grps.. i ca n do it by pla cing 2 stick s ..fo r tha t i ha ve to ta l o f |*|*|*|*|*|

--> | de no te s cho ice s

6 cho ice s.. so se le cting 2 spa ce s o ut o f 6 ca n be do ne in 6C 2 = 15 wa ys.. te l m e wa ts go in wro ng in this a ppro a ch..

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Re: Permutation and Combination by sum it ja m wa l - T hursda y, 12 Fe brua ry 2009, 09:41 P M hi T G, the pro ble m i ha d a bo ve , i'd do ne a m ista k e a ctua lly thr wud be 30 wa ys ... fo r 1st stick - 6 wa ys fo r 2nd stick - 5 so to ta l - 6*5=30. if yo u cud cla rify this thing it wud be nice R e ga rds, sum it S how parent | R eply

Re: Permutation and Combination by T o ta l Ga dha - T hursda y, 12 Fe brua ry 2009, 11:09 P M Hi Sum it, In yo ur so lutio n, yo u ca n't pla ce stick s lik e this fo r e x a m ple ||* * * * * T his wo uld de no te a 0 0 5 ca se which yo u ca nno t co ve r. Y o u ca n o nly co ve r 0 5 0 ca se by pla cing the stick s in this m a nne r: |* * * * *| T he wa y yo u a re pla cing the stick s yo u ca n ne ve r pla ce two stick s side by side be ca use yo u a re ta k ing it to be o ne spa ce o nly. T o ta l Ga dha S how parent | R eply

Re: Permutation and Combination by sum it ja m wa l - Frida y, 13 Fe brua ry 2009, 12:16 AM hi sir, sir tha t's fine ..bt if ia m nt co nside ring this ca se ..the n y is m y a nswe r co m in to be a rnd 30 ..whr a s u sta te d it's 21. i think thr m ight be so m e k ind o f re pe a titio n... a nd a s u to ld | | * * * * * nt include d so , no w suppo se i pla ce 1st stick the n a rra nge m e nt wud be lik e .. | * * * * * no w to include ur ca se fo r 2nd stick thr a re 6 ca se s a s i ca n pla ce stick be twe e n sta rs a nd be side 1st stick

in this ca se to ta l ca se s co m e o ut to be 36

still m o re tha n 21

a bit co nfuse d a s ho w to ge t co rre ct re sult by using this stick m e tho d.

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Re: Permutation and Combination by T o ta l Ga dha - Frida y, 13 Fe brua ry 2009, 09:32 AM Hi Sum it, T he re pe titio n is be ca use yo u a re ta k ing pa rtitio ns to be diffe re nt whe re a s the re ha ve to be ta k e n a s sim ila r. Fo r e x a m ple , ta k e two sim ple ca se s: * P 1 * * * P 2 * a nd * P 2 * * * P 1 * whe re P 1 a nd P 2 de no te the pa rtitio ns. Bo th the se ca se wo uld yie ld the sa m e re sult, i.e . 1 3 1 but yo u a re co unting the m a s diffe re nt. If I do this by yo ur m e tho d I will do it lik e this: Fo r the first pa rtitio n I ha ve 6 pla ce s. * * | * * * Fo r the se co nd pa rtitio n I ha ve 7 pla ce s. T he re fo re to ta l num be r o f wa ys = 6 × 7 = 42. As e a ch ca se is be ing re pe a te d o nce , the to ta l num be r o f ca se s = 42/2 = 21. T o ta l Ga dha S how parent | R eply

Re: Permutation and Combination by sum it ja m wa l - Frida y, 13 Fe brua ry 2009, 05:07 P M hi T G, tha nk s

,tha t wa s wa t i think ing....

gr8 wo rk .. R e ga rds , sum it S how parent | R eply

Re: Permutation and Combination by Abhina v Kum a r - Frida y, 22 Ma y 2009, 01:38 P M

T ha ts re a lly a be a utiful o ne . Ma de such a difficult ta sk so sim ple with the e x a m ple s o f such a va rie ty. T ha nk s a Lo t Abnv

S how parent | R eply

Re: Permutation and Combination by ro ny ro y - Frida y, 22 Ma y 2009, 02:33 P M hi T G, wha t wa s the a nswe r to the que stio n tha t go e s..... ho w m a ny a rra nge m e nts o f six 0s five 1s a nd fo ur 2s a re the re in which ii)the first 0 pre ce de s the first 1,(a nd) pre ce de s the first 2. m y a nswe r co m e s o ut to be a m a ssive : 504504

re ply so o n... S how parent | R eply

Re: Permutation and Combination by iim fre a k - T ue sda y, 26 Ma y 2009, 12:29 P M

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions hi tg.. 1st o f a ll tha nk s a to n fo r this sim ply a we so m e po st .. i ws nt ge tting a ny gud m a te ria l o n P &C n P ro ba bility n wa s wo rrie d ... tha nk s a ga in.. .. re ga rding the Problem :: the re a re 10 spe a k e rs who r suppo se d 2 a ddre ss. O ne co nstra int is P M shud a ddre ss be fo re MP a nd MP be fo re MLA . My soln:: Le t P M = P ; MP = Q ; MLA = R the o rde r shud be P Q R .. so i tuk P Q R a s 1 blo ck a nd so to ta l pe o ple 2 b a rra nge d be co m e s (7+1) = 8 ... a nd no w a rra nging the m we ge t A ns = 8! . P le a se te ll whe re a m i m a k ing the m ista k e ?

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Re: Permutation and Combination by P riye sh T unga re - W e dne sda y, 27 Ma y 2009, 02:59 P M Hi T G,

T ha nk s fo r the a rticle . I ha ve o ne do ubt. In the que stio n, Ho w m a ny 3-digit num be rs a re e ve n a nd with no re pe a te d digits, in the se co nd ca se fo r num be r no t e nding in 0, yo u ha ve m ultiplie d 8*8*4. C a n yo u e x pla in why we a re m ultiplying 4 he re ? T his m a y be sim ple que stio n fo r o the rs, bt i be lie ve in sa ying.. whe n in do ubt a sk .... T ha nk s, P riye sh T unga re S how parent | R eply

Re: Permutation and Combination by T o ta l Ga dha - T hursda y, 28 Ma y 2009, 02:06 P M Hi R a nde e p, 'Be fo re ' m ight no t a lwa ys m e a n 'just be fo re ,' a s yo u ha ve a ssum e d by ta k ing the m to ge the r. T he re ca n be o the r pe rso ns be twe e n P , Q a nd R. T o ta l Ga dha S how parent | R eply

Re: Permutation and Combination by T o ta l Ga dha - T hursda y, 28 Ma y 2009, 02:08 P M Hi P riye sh, T he re a re fo ur 4 e ve n digits a fte r re m o ving ze ro - 2, 4, 6 a nd 8. T he num be r wo uld e nd in o ne o f the se . T o ta l Ga dha S how parent | R eply

Re: Permutation and Combination by iim fre a k - T hursda y, 28 Ma y 2009, 10:21 P M o h ye a h ,, go sh i shud ha v tho t da t.. tha nk s a lo t fo r cle a ring the do ubt ... T G sir it will b a gr8 he lp if u cud po st so m e gud te x t, lik e dis, fo r P ro ba blity a lso .. da ts a no the r a re a , which i find to ugh.. S how parent | R eply

Re: Permutation and Combination by iim fre a k - Frida y, 29 Ma y 2009, 10:09 AM hi tg.. fro m whe re ca n i find the a nswe rs 2 the a bo ve e x e rcise .. its v im p 2 chk whe the r i ha v unde rstud ur co nce pts pr nt. S how parent | R eply

Re: Permutation and Combination

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hi tg, im a bit co nfse d wid the so lutio n to the pa int cube pro ble m ............ the firstfa ce wich we cho o se cn b pa inte d in 6 wa ys,.........y ha ve nt u co nside re d tha t....plzzz e nlighte n S how parent | R eply

Re: Permutation and Combination by Avishe k C ha k ra bo rty - T hursda y, 11 June 2009, 07:39 P M He y guys I ha ve a que stio n re la te d to this to pic, co uld u so lve this? He re it go e s... Q . 4 bo yz n 4 girls a re a rra nge d in a ro w so tha t no 2 girls a re to ge the r.W a t is the pro ba bility tha t a ny 2 bo yz a re to ge the r? wa iting fo r ur re spo nse ... S how parent | R eply

Re: Permutation and Combination by iim fre a k - T hursda y, 11 June 2009, 08:27 P M dude .. this is P nC thre a d n u a sk ing P ro ba bility ..jst k idding .. a nywa ys i dnt k no w pro ba bility so ca nt he lp @ this m o m e nt .. T G sir will be po sting a te x t o n P ro b so o n... wa iting fo r tha t...AT B m a te S how parent | R eply

Re: Permutation and Combination by k u k lux k la n - T hursda y, 18 June 2009, 07:18 P M the re a re 4 frie nds a nd 10 ho te l ro o m s q)in ho w m a ny wa ys ca n a t le a st two frie nds sta y to ge the r m y a nswe r to this is a s fo llo ws,which is le a ding m e to the wro ng a nswe r,will be ve ry gra te ful if so m e o ne ca n po int o ut the fa lla cy in this 1 ca se )-2 frie nds sta y to ge the r c(4,2)*10*9*8 2nd ca se )thre e frie nds sta y to ge the r c(4,3)*10*9 3rd ca se )a ll fo ur sta y to ge the r 10 a dding up a ll the se ca se s i a m ge tting 4690,which is wro ng....ple a se te ll m e the m ista k e in this S how parent | R eply

Re: Permutation and Combination by ro ha n k a usha l - Sa turda y, 20 June 2009, 09:03 AM hi, Q.

ho w m a ny thre e digit num be rs a re the re which a re e ve n a nd ha ve no re pe a te d digits ????

ca n't it be this wa y??? _ _ _ the 3rd pla ce 5 cho ice s ,(i.e ; 0,2,4,6,8) so no o f wa ys a re 5 1st pla ce ha ve 8 cho ice s (e x cluding 0 a nd the 3rd pla ce 's num be r) & 2nd pla ce ha ve a ga in e ight cho ice s .... a nd tha t co m e s o ut to be 8 * 8 * 5 = 320 .. co uld yo u plz he lp m e ....... tha nx a lo t!!!! S how parent | R eply

Re: Permutation and Combination by a m it ja in - Sunda y, 21 June 2009, 12:37 P M @R o ha n, W he n yo u will use 0 fo r the unit's pla ce the n fo r the hundre ds pla ce yo u will ha ve 9 cho ice s(1....9) a nd 1o th pla ce 8 cho ice s. I ho pe no w yo u k no w whe re yo u a re ge tting it wro ng S how parent | R eply

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Re: Permutation and Combination by sm ruty pa nigra hi - Mo nda y, 13 July 2009, 11:10 AM

Hii, T his is a ra the r sim ple lo o k ing pro ble m but ha s be e n pe ste ring m e a nd a m una ble to so lve . P l che ch it o ut a nd he lp m e guys. Y o u ha ve to find o ut the num be r o f wa ys to re a ch fro m A to B. Ex tre m e ly so rry 4 the po o r qua lity o f fig. I a in't tha t go o d with co m pute rs. P lz give a de ta ile d so lutio n. T ha nx in a dva nce .

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Re: Permutation and Combination by a rya n ra j - Mo nda y, 13 July 2009, 03:03 P M hi sir this file is so go o d fo r ca t e x a m so i wa nt so lutio n o f the a ll pro b so plz sa nd m e the so lutio n o n m y e m a il S how parent | R eply

Re: Permutation and Combination by Ank it Me go tia - T ue sda y, 28 July 2009, 11:13 AM he y sm ruty, by a ny cha nce do yo u k no w the a nswe r to yo ur que stio n?

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions its co m ing o ut to be 72. if its co rre ct i will te ll yo u the pro ce dure . S how parent | R eply

Re: Permutation and Combination by Ja ide e p Da s - T ue sda y, 28 July 2009, 10:44 P M

C a n so m e bo dy pro vide m e the a nswe rs fo r (ii) a nd (iii) pa rts o f the que stio n fo r 6 0's, 5 1's a ns 4 2's? I go t the a nswe rs a s 15840 fo r (ii) a nd 378738 fo r (iii) Are the se a nswe rs co rre ct? P le a se re ply S how parent | R eply

Re: Permutation and Combination by Go wtha m Muthuk k um a ra n T hiruna vuk k a ra su - Mo nda y, 3 August 2009, 11:20 P M Y o u r right. T he so lutio n give n he re , is ba se d o n a a ssum ptio n tha t the thre e spe e k in o rde r, which is no t the ca se . Y o ur so lutio n is pe rfe ct i gue ss. S how parent | R eply

Re: Permutation and Combination to Bheemesh K by Go wtha m Muthuk k um a ra n T hiruna vuk k a ra su - Mo nda y, 3 August 2009, 11:22 P M Y o u r right. T he so lutio n give n he re , is ba se d o n a a ssum ptio n tha t the thre e spe e k in o rde r, which is no t the ca se . Y o ur so lutio n is pe rfe ct i gue ss. S how parent | R eply

Re: Permutation and Combination TO smruty panigrahi by Go wtha m Muthuk k um a ra n T hiruna vuk k a ra su - T ue sda y, 4 August 2009, 12:31 AM

Fro m the figure yo u ha ve give n i ha ve wo rk e d o ut a nd go t the a nswe r to be 30. Juz che ck if yo u a lre a dy k no w the a nswe r a nd if it is wro ng ple a se le t m e k no w. I ha ve a tta che d the file he re . Mo re o ve r I ha ve a ssum e d tha t o ne ca n tra ve l thro ugh a pa th o nly o nce . Fo r e x a m ple yo u ca nno t go thro ugh ED a nd a ga in co m e ba ck to E.

S how parent | R eply

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions Re: Permutation and Combination by Avishe k C ha k ra bo rty - W e dne sda y, 5 August 2009, 03:31 P M

Firstly i m ust sa y the a rticle is a we so m e ! P le a se pa rdo n m e if m y que stio n se e m s childish! T he re 's o ne que stio n re la te d to dice , in ho w m a ny wa ys sum o f 8 ca n be o bta ine d by ro lling 2 dice if the the y a re distinguisha ble ... no w m y que stio n is a s we a re rightly co nside ring (3,5) a nd (5,3) a s diffe re nt ca se s, why a re we no t ta k ing two ca se s fo r (4,4)? T ho ugh the de no m ina tio ns a re sa m e but the dice a re distinguisha ble . S how parent | R eply

Re: Permutation and Combination by ca t cha m p - Sa turda y, 8 August 2009, 04:11 P M i do nt think it will be ta k e n a bhishe k .. a s(4,4) is m a k ing the dice indistinguisha ble .. btw.. ve ry go o d wo rk tg sir..the be st a rticle till da te i ha ve fo und o n p&c.. a nd i will be po sting the so lns so o n.. S how parent | R eply

Re: Permutation and Combination by a nim e sh cha nda n - Sa turda y, 15 August 2009, 10:57 P M hi T G i ha v pro ble m Q :the re a re 7 m e n a nd 5 wo m e n we ha ve to se le ct 4 m e n a nd 3 wo m e n but if m rs A will go the n m rs B will no t go .in ho w m a ny wa ys v ca n se le ct the m ? m y a ppro a ch is 7 m e n will be se le cte d in 7C 4 wa ys a nd the re a re 3 ca se s ca se 1: we first se le ct m rs A the m a uto m a tica lly m rs b will no t be se le cte d the n we ca n se le ct re m a ining wo m e n in 3C 2 wa ys, tha t is 7C 4*3C 2=105. ca se 2: we se le ct m rs B the n a uto m a tica lly m rs A will no t be se le cte d the n ve ca n se le ct re m a ining wo m e n in 3C 2 wa ys, tha t is 7C 4*3C 2=105, ca se 3:if bo th o f the m a re no t se le cte d the n we will ha ve 3C 3 wa ys to se le ct wo m e n tha t is 7C 4*3C 3=35 tha t m e a ns to ta l no o f wa ys =105+105+35=245 plZZZ te l m e is it the right a ppro a ch????? S how parent | R eply

Re: Permutation and Combination by Ano o p Ma itha ni - T hursda y, 20 August 2009, 10:30 AM Hi T G.. Am a zing a rticle ..wa iting e a ge rly fo r a n a rticle o n P ro ba bility.. S how parent | R eply

Re: Permutation and Combination by Be llT he C AT ... - T hursda y, 20 August 2009, 07:18 P M Hi T G, A re a lly he lpful a rticle ,fo r it he lpe d m e re vise P &C . tha nk s a lo t. S how parent | R eply

Re: Permutation and Combination by de e p sin - Sa turda y, 5 Se pte m be r 2009, 01:59 P M @ k u k lux k la n Y o u a re fo rge tting to ta k e o ne ca se into ca lcula tio n T he ca se is : - 2 sta y in sa m e ho te l a nd re m a ining 2 a lso sta ys in sa m e ho te l. S how parent | R eply

Re: Permutation and Combination by P a lla v Ja in - T hursda y, 17 Se pte m be r 2009, 07:03 P M Hi All, C a n yo u plz te ll m e the so lutio n ? Using o ne o r m o re o f the digits 1, 2, 3, 4, 5, 6 a nd 7, ho w m a ny 7-digit num be rs ca n be fo rm e d which a re divisible by 7?

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions O ptio ns :A) 7 5 + 7 4 + 7 3 + 7 2 + 7 B) 4 × 7

5

C ) 4 × 76 D)

76

E)

6 × 76

Thanks Pallav Jain

S how parent | R eply

Re: Permutation and Combination by priya ra m ra j - Frida y, 18 Se pte m be r 2009, 04:00 P M Hi T G, I ha ve a do ubt in the a rticle tha t u ha ve po ste d. T o ge t a sum o f 8 with distinguisha ble dice s, wo nt the o ccurre nce o f(4,4) be diffe re nt be ca use it is distinguisha ble ??? shudnt we co nside r it a s 2 ca se s ..P ls cla rify... S how parent | R eply

Re: Permutation and Combination by R O HIT K - Frida y, 18 Se pte m be r 2009, 05:05 P M Hi priya, Jus to giv it a try.. To get a sum of 8 with distinguishable dices, wont the occurrence of(4,4) be different because it is distinguishable??? shudnt we consider it as 2 cases .. (2,1) a nd (1,2) a re diffe re nt in distinguisha ble dice (which is no t the ca se in sa m e k ind o f dice ). Sa y, yo u ha ve a re d a nd a blue die C a se : (1,2) a nd (2,1) 1.R e d->1 Blue ->2 2.R e d->2 Blue ->1 Y o u ca n distinguish the two no t o nly by the ir co lo r but a lso by the diffe re nce in the ir num e rica l va lue . C a se 2: (4,4) 1.Blue ->4 R e d->4 2.R e d->4 Blue ->4 Are n't the y bo th sa m e ?? If ye s, the n we ne e d no t co nside r it two ca se s. In sho rt, since the num e rica l va lue is sa m e , we ca nno t distinguish the ca se tho ugh the two dice a re distinguisha ble . Ho pe this he lps. R o hit

P .S if yo u still didn't unde rsta nd...T G to ha i..!! S how parent | R eply

Re: Permutation and Combination by priya ra m ra j - Frida y, 18 Se pte m be r 2009, 05:31 P M Hi R o hit, go ing by ur e x a m ple ,W a t i unde rsta nd fro m the a rticle is tha t co lo r is the distinguishing fa cto r a nd no t the num be r... If we re m o ve the co lo r a spe ct fro m the a rgum e nt o nly the n the distinguishing pro pe rty va nishe s... ho pe i a m no t wro ng..a nywa ys.. T ha nk s fo r the a ppro a ch S how parent | R eply

Re: Permutation and Combination by R O HIT K - Sa turda y, 19 Se pte m be r 2009, 02:17 P M Hi priya, Color is the distinguishing factor and not the number... If we remove the color aspect from the argument only then the distinguishing property vanishes... I do no t co m ple te ly a gre e with yo ur co nclusio n.. T he dice ha d two diffe re nt co lo rs viz. re d a nd blue ..(I did no t re m o ve the m ) But, still yo u co uld no t distinguish fro m e a ch o the r..!!(ho w co uld yo u if the y a re the sa m e o ne s?)

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions T he re a so n wa s no t co lo r but sa m e num e rica l va lue .. If yo u ha d cha nge d the num be r to the n yo u wo uld ha ve distinguishe d it fro m o ccurre nce . if yo u ca n che ck m y e x pla na tio n a ga in a fte r re a ding this ho pe it wo uld be m o re cle a r.. 1. If co lo rs o f dice a re sa m e (i.e indistinguisha ble dice ) the n o ccurre nce o f o r o r fo r tha t m a tte r a ny pa ir o f va lue s a nd vice ve rsa ca nno t be distinguishe d..(ve ry o bvio us) (indistinguisha ble be ca use o f co lo r) 2. If co lo rs o f dice a re diffe re nt the n a . ca n be distinguishe d fro m o ccurre nce o f (distinguisha ble be ca use o f co lo r o f the dice ) b. o r fo r tha t m a tte r a ny sa m e va lue o n bo th dice ca nno t be distinguishe d fro m vice ve rsa va lue (which is a ctua lly the sa m e o ccurre nce a s the pre vio us..) (indistinguisha ble be ca use o f sa m e va lue o n the dice ) He nce , the co nclusio n ca n be dra wn tha t the distinguishing fa cto r in the dice o f diffe re nt co lo rs is the co lo r a spe ct, o nly whe n num be rs a ppe a ring o n the dice a re diffe re nt. If the num be r be co m e s sa m e (indistinguisha ble ) the n yo u ca nno t distinguish the o ccurre nce . Ho pe this he lps.. R o hit S how parent | R eply

Re: Permutation and Combination by Sure sh S - Mo nda y, 21 Se pte m be r 2009, 11:11 AM Hi sir .. its re a lly supe rb.... tha nk s fo r ur a rticle ..... S how parent | R eply

Re: Permutation and Combination by R O HIT K - T ue sda y, 22 Se pte m be r 2009, 12:36 P M Hi T G..!! T ha nk s fo r such a nice a rticle . I ha d o ne que stio n re ga rding: In ho w m a ny wa ys ca n 4 pe rso ns be se a te d o ut o f 5 bo ys a nd 3 girls in 4 diffe re nt se a ts? W hile e x pla ining yo u sa id it is not the sim ple fo rm ula ba se d P &C pro ble m . T ho ugh, I think tha t it co uld be so lve d in ve ry sim ple te rm s witho ut bre a k ing do wn the pro ble m into ca se s(the wa y yo u a lre a dy sugge ste d a s the co nce pt). T wo a spe cts to this pro ble m : 1. Se le cting 4 pe rso ns fro m 8 pe rso ns(5 bo ys+3 girls) which ca n be do ne in 8C 4 wa ys 2. Arra nging the 4 pe rso ns o n 4 diffe re nt se a ts fo r e a ch se le ctio n which ca n be do ne in 4! wa ys So to ta l num be r o f wa ys = 8C 4 * 4! = 70*24 = 1680 (sa m e a s 8P 4) P le a se le t m e k no w if this is no t the right wa y to a ppro a ch the pro ble m . I ne e d yo ur insight into this. T ha nk s a nd R e ga rds R o hit S how parent | R eply

Re: Permutation and Combination by R o ha n S - T ue sda y, 29 Se pte m be r 2009, 11:49 AM

T G ST ANDS FO R T R UE GUIDE........ S how parent | R eply

Re: Permutation and Combination by sha rm ishtha Gupta - Frida y, 9 O cto be r 2009, 01:13 P M Hi,

supe rb a rticle . i ha ve a do ubt tho ugh, in the que s whe re u hv 10 co lle ge stude nts , 5 bo ys a nd 5 girls a nd u ha ve to m a k e sure tha t no two girls sit to ge the r,

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions ca n we first m a k e the bo ys sit in 5! wa ys _B_B_B_B_B_ no w, fo r the girls to sit , we ha ve to cho o se 5 o f the 6 pla ce s a va ila ble so tha t no two girls sit to ge the r, this ca n be do ne in 6 wa ys a nd the girls ca n the n be se a te d in 6* 5! wa ys. T he re fo re , the no o f wa ys in which the y ca n sit a cco rding to the give n co nditio n the n co m e s o ut to be 6*5!*5!.

P le a se co rre ct m e if i a m wro ng. T ha nx S how parent | R eply

Re: Permutation and Combination by AsHwIn Drm z - Sa turda y, 10 O cto be r 2009, 01:32 AM hi Sha rm ista , Y o u a re m issing o ut so m e hig he re . Sa y 1st we se a t a ll the bo ys..in 5! wa ys. T he n we ha ve 6 pla ce s whe re 5 girls ha ve to be se a te d.No w, 1st girl ca n be se a te d in a ny o f the 6 a va ila ble pla ce s,2nd girl ca n be se a te d in the re m a ining 5 a va ia lble pla ce s ,3rd girl ca n be se a te d in re m a ining 4 a va ila ble pla ce s....e tc ie 6 x 5 x 4 x 3 x 2 . so to ta l a rra nge m e nts bo ils do wn to : 2 * 5! *(6x 5x 4x 3x 2) Ho pe its cle a r no w. Ashwin S how parent | R eply

Re: Permutation and Combination by sha rm ishtha Gupta - Sa turda y, 10 O cto be r 2009, 10:03 P M T ha nx a shwin. U m ight think m e to be a dud but k indly e x pla in ho w u go t the 2 in 2*5!*(6*5*4*3*2) . S how parent | R eply

Re: Permutation and Combination by AsHwIn Drm z - Sa turda y, 10 O cto be r 2009, 10:59 P M he y.. do nt think lik e da t..W e a re a ll he re to le a rn fro m e a cho the r no o ne is pe rfe ct.So ne ve r unde re stim a te urse lf...C o m ing to the que stio n, se e the re will be 2 ca se s :1st ca se whe n u se a t a ll the bo ys 1st in 5 pla ce s the n a rra nge the girls .2nd ca se yo u ca n se a t the girls 1st the n a rra nge the bo ys a m o ng the m . he nce we ta k e 2* Ho pe its cle a r no w. Ashwin S how parent | R eply

Re: Permutation and Combination by Sa ra va na r B - W e dne sda y, 21 O cto be r 2009, 01:24 P M

Hi TG Sir, Thanks a lot for your article and I don't have any words to describe ur work sir... I owe a lot... Great job sir... I have a great respect for you sir and long live TG family Have a small doubt sir : 1. Four friends go to a city in w hich there are 10 hotels. In how many w ays can they stay ?

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Sol : (approach 1) : The first friend can stay in 10 ways, the second friend can stay in 10 ways, similarly the third and fourth.. so the ans is 10*10*10*10 = 10000 (approach 2) : The first hotel can accomodate 4 friends or 3 friends or 2 friends or 1 friend or 0(zero). So nu of ways the 1st hotel can accomodate is 1+2+3+4 = 10 ( i have added 1,2,3,4 as it is either - "OR" case) Same goes for 2nd hotel, 3rd hotel and 4th hotel... so the ans is 10*10*10*10 = 10000 ******************************************************* Now have a look at question no 2 ******************************************************* 2. In how many w ays can u post 10 letters in 4 letterboxes ? Sol : ( approach 1 ) The first letter can be posted in 4 ways, similarly the second,third....tenth. So the ans is : 4*4*4...*4 = 4^10 = 1048576

(approach 2 ) : The first letter box can get '1' or '2' or '3' ..... '10' letters.So nu of ways the 1st letter can accomodate is 1+2+3+4+..+10 = 55 Same goes for 2nd letter 3rd letter and 4th letter so the ans should be 55*55*55*55= 9150625 Doubt : I couldn't figure out what is wrong with my second approach.. Kindly explain me sir.. Also tell me given a question when to apply which approach... My prob is I never get satisfied with one approach sir.. I always try out different approach.. I am sure ur explanation would be helpful to many of the students like me... Thanks Saran S how parent | R eply

Re: Permutation and Combination by T o ta l Ga dha - W e dne sda y, 21 O cto be r 2009, 09:42 P M

Hi Saravanar, If first letter box posts even 1 letter or 2 letters etc . the sec ond letter box does not have 10 ways. Total Gadha S how parent | R eply

Re: Permutation and Combination by sk ysk ie rs 44 - Mo nda y, 26 O cto be r 2009, 02:55 AM He llo ,

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions m no t sure if this is the right se ctio n to po st pe rm uta tio n pro ble m , but a nywa ys ple a se he lp m e o ut with the fo llo wing In ho w m a ny wa ys ca n 10 so ldie rs sta nd in 2 ro ws such tha t the re a re 5 so ldie rs in e a ch ro w? Is the a nswe r 7257600 o r 7257600/2 ? P une e t S how parent | R eply

Re: Permutation and Combination by Na ba nshu Bha tta cha rje e - T ue sda y, 27 O cto be r 2009, 01:33 AM Hi T G T ha nk s a ga in, W a nte d to sha re the pro ba bilistic a ppro a ch to de a rra nge m e nt pro ble m with the T Gite s. http://m a thfo rum .o rg/libra ry/drm a th/vie w/56592.htm l A que ry: If yo u go thro ugh the pro o f in the link I ha ve give n, yo u ca n se e tha t the y a re co nside ring 4 o ut o f 5 le tte rs pla ce d in the co rre ct e nve lo pe . Ho w co m e the re re sult m a tche s with the o ne give n in this thre a d? I m e a n i co uld no t find whe re I a m go ing wro ng. P le a se he lp!!! S how parent | R eply

Re: Permutation and Combination by Sa ra va na r B - Frida y, 30 O cto be r 2009, 12:26 AM Hi T G, T ha nk s fo r yo ur re ply... Y e s i go t it... the se co nd le tte r bo x ne e d no t ha ve te n wa ys... Is the re a wa y to so lve this que stio n in the letter box perspective (approach 2) ?? I trie d to so lve but co uldn't ge t the a ns a s we ll a s the a ppro a ch.. Sa ra n S how parent | R eply

Re: Permutation and Combination by swe tha chintha re ddy - Mo nda y, 2 No ve m be r 2009, 03:35 P M 6 Ba lls o f diffe re nt co lo urs a re to be distribute d a m o ng 2 bo ys. W ha t is the pro ba bility tha t e a ch bo y ge ts sa m e num be r o f ba lls? a ) 5/16 b) 15/64 c) 1/2 d) 3/8 S how parent | R eply

Re: Permutation and Combination by nishcha i ne vre k a r - W e dne sda y, 4 No ve m be r 2009, 05:58 P M Hi, I wo uld lik e to po int o ut the tha t the so lutio n to the 5 BO Y , 5 GIR L MO VIE m o vie pro ble m with no girls sitting to ge the r is a little fla we d... It do e snt ta k e in to co nside ra tio n this a rra nge m e nt

GBGBGBBGBG n m a ny o the rs lik this.... so the soln to this has to be considered by keeping objects (or people for this problem) who are not supposed to be together as dynamic and others as static... he re bo ys ha ve to be sta tic n girls dyna m ic... a s sho wn be lo w

_B_B_B_B_B_

so girls o nly ha ve six po sitio ns to go into a nd a lso the y will ne ve r be to ge the r a s we lim iting the m by pro viding o nly o ne slo t btw bo ys. He nce re fe r to the m a s dyna m ic a s the y ca n ta k e 6 po sitio ns. so , 6P5 = 6x 120 while bo ys who ca n be to ge the r a re sta tic ca use the y ca n o nly ta k e 5 po sitio ns. 5P5 = 120 so , to ta l no wa ys = 120x 120x 6 = 14400x 6 Ho pe this wa s he lpful... Also , P le a se co rre ct m e if I a m wro ng :D S how parent | R eply

Re: Permutation and Combination by T o ta l Ga dha - Frida y, 6 No ve m be r 2009, 01:46 P M

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Hi Nishc hal, You forgot the c ondition mentioned in the question- every boy wants to sit with a girl. Total Gadha S how parent | R eply

Re: Permutation and Combination by sa ura bh pra bhude ssa i - Frida y, 6 No ve m be r 2009, 03:42 P M in the co nditio n m e ntio ne d by nischa i e ve ry bo y ha s a t le a st o ne ga l o n his side !! S how parent | R eply

Re: Permutation and Combination by nishcha i ne vre k a r - Frida y, 6 No ve m be r 2009, 03:59 P M in the se type s o f a rra nge m e nts

GB GB BG BG BG

Here every boy is sitting with one girl.... it the condition was "every boy wants to sit in-between 2 girls" then i would be a diff case altogether. If not then plz temme... y these cases are not to be considered... S how parent | R eply

Re: Permutation and Combination by vine e t ja in - T ue sda y, 17 No ve m be r 2009, 12:41 AM Hi T G!! supe rb a rticle I ha ve a que stio n which ha s be e n a sk e d by R o hit a lso .i a m using sa m e la ngua ge a s him "In ho w m a ny wa ys ca n 4 pe rso ns be se a te d o ut o f 5 bo ys a nd 3 girls in 4 diffe re nt se a ts? W hile e x pla ining yo u sa id it is no t the sim ple fo rm ula ba se d P &C pro ble m . T ho ugh, I think tha t it co uld be so lve d in ve ry sim ple te rm s witho ut bre a k ing do wn the pro ble m into ca se s(the wa y yo u a lre a dy sugge ste d a s the co nce pt). T wo a spe cts to this pro ble m : 1. Se le cting 4 pe rso ns fro m 8 pe rso ns(5 bo ys+3 girls) which ca n be do ne in 8C 4 wa ys 2. Arra nging the 4 pe rso ns o n 4 diffe re nt se a ts fo r e a ch se le ctio n which ca n be do ne in 4! wa ys So to ta l num be r o f wa ys = 8C 4 * 4! = 70*24 = 1680 (sa m e a s 8P 4)" ple a se co rre ct m e if i a m do ing it wro ng S how parent | R eply

Re: Permutation and Combination by SHAUNAK A - T ue sda y, 24 No ve m be r 2009, 08:16 P M He llo T G sir, T ha t's C AT lik e a rticle o n P e rm C o m ......sim plicity e x e m plifie d... T ha nx Sir... S how parent | R eply

Re: Permutation and Combination by Ha rish A - W e dne sda y, 25 No ve m be r 2009, 09:32 P M Hi T G, T his is My first po st in this is fo rum . It is gre a t disa ppo intm e nt I wo uld lik e sa y, e ve n a fte r go ing thro ugh the Le sso ns m ultiple tim e s, I a m una ble to so lve e ve n a single pro ble m . It is no t be ca use o f the wa y yo u e x pla in things, but it is m y a bility. I a m sure with the se give n se t o f sk ills, I a m ill e quippe d to ta ck le C AT . It m a y be o f gre a t he lp if yo u ca n le t m e whe re the so lutio ns a re pre se nt I ca n just re a d the m fo r purpo se o f le a rning. T ha nk s, Ha rish.A S how parent | R eply

Re: Permutation and Combination by a ritre ye e cha udhuri - W e dne sda y, 2 De ce m be r 2009, 08:50 P M

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions Hi T G I lo ve d this a rticle ..tha nk s a lo t fo r ur e ffo rts

..this he lpe d m e re co lle ct m a ny o f the co nce pts le a rnt e a rlie r..

but i a m no t cle a r a bo ut the 'pa inting fa ce s o f a cube ' pro ble m ..two o the r guys Syd S a nd Anirba n Bha r ha ve a lso a sk e d the sa m e que stio n tha t i a m go ing to type no w.. W he n we fix the co lo r o f o ne side o f a cube ..we ha ve 6 po ssibilitie s (a s the re a re six co lo rs)..a nd in tha t ca se the o ppo site side will ha ve 5 po ssibilitie s..fo r the re m a ining we ca n use the circula r pe rrm uta tio n rule ..so the re m a ining side s ca n be pa inte d in (4-1)! wa ys.. So sho uldnt the num be r o f wa ys in which the cube ca n be pa inte d, be 6x 5x 3! ? C a n u ple a se cla rify this? S how parent | R eply

Re: Permutation and Combination by gurte z singh - T hursda y, 11 Fe brua ry 2010, 05:56 P M nice wo rk sir ........... i hve a pro b... ~ the re r fo ur se ctio ns o f a pa pe r wid a m a x . m a rk s f 45 fr e a ch se ctio n & to qua lify 1 ha ve ge t m in. 90 m a rk s the n in hw m a ny wa ys he cn qua lify da e x a m ?????????????? S how parent | R eply

Re: Permutation and Combination by vija yshre e m e no n - Mo nda y, 5 April 2010, 10:05 P M Hi , C a n a ny1 e x pla in m e this In the a bo ve po st , T G sir cite d a n e g @ an election meeting 100 ppl address rally. Order followed PM then MP followed by MLA So lutio n give n: Le t P M = P MP de no te d a s Q a nd MLA a s R . 10 spe a k e rs a dddre ss ra lly in 10! wa ys. this include s P Q R P R Q Q P R Q R P R P Q R Q P . No w Since ne e d o nly P Q R we divide 10! by 6. I ha ve a ge nuine pro b he re . First o f a ll its de cide d ta t P Q R will be the o rde r which m e a ns we ne e d to k e e p P Q R fix e d a nd o nly co unt the re m a ining 7 ppl a rra nge m e nt. Y ca nt it be so ??? I k no w I wro ng whe re a m I m a k ing the m ista k e .... Im a re a l dum b o ne to ha ve such do ubts ... but wa nt to m a k e it cle a r .... P ls T G sir o r Da gny Ma m o r who e ve r ca m a m swe r this q P ls he lp P ls...

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Re: Permutation and Combination by Aspire nd Achie ve - Mo nda y, 10 Ma y 2010, 02:27 P M Hi T G Sir, ca n yo u ple a se e x pla in the so lutio n fo r pro ble m 3 S how parent | R eply

circular -linera query by ro bin ca tch - Frida y, 25 June 2010, 03:41 P M

DEAR TG..help me on this?? the number of ways that 4 girls and 5 boys can sit around a table st no two girls sit together ? is there a general formula?? what would be the solution for a linear table, ie 4 girls and 5 boys( no 2 girls sit together)?? what would be the soln had 2 girls been always together, http://totalgadha.com/mod/forum/discuss.php?d=3537

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(case1:around a round table case 2: in a linear arrangement)??? thnx in advance, highly appreciate for quick reply imlovinmath S how parent | R eply

A nswers by R a m it Go ya l - Mo nda y, 28 June 2010, 11:04 P M 1 a 2 b 3 d 4 c 5 c 6 a 7 d 8 c 9 c 10 b 11 b 12 c 13 14 a 15 16 17 b 18 d 19 a 20 c P le a se re vie w a nd no tify m e fo r una tte m pte d que stio ns a nd wro ng a nswe rs S how parent | R eply

Re: Permutation and Combination by so na li pa wa r - T hursda y, 8 July 2010, 03:12 P M Hi T G, As usua l be a utiful a rticle !!!! Just o ne do ubt...... In the pa rt o f Distributio n in the pro ble m o f 5 ba lls a nd 3 bo x e s ca se IV i.e whe n a ll ba lls a nd bo x e s a re dissim ila r, fo r distributio n 113 a nd 122 u sa y the no o f distributio ns a re 3!. Sho uldn't it be 3!/2! = 3 a s the re a re 2 gro ups with sa m e num be r o f things? P le a se co rre ct m e if m wro ng! S how parent | R eply

Re: Permutation and Combination by T G T e a m - T hursda y, 8 July 2010, 05:32 P M

Hi Sonali Though in 113 and 122 distribution there are two groups with same number of things but still they are different groups bec ause of different balls. That's why it is 3! in plac e of 3!/2! Hope it is c lear. S how parent | R eply

Re: Permutation and Combination by Na m a n Mircha nda ni - T ue sda y, 20 July 2010, 04:29 P M

Sir, I have one confusion: http://totalgadha.com/mod/forum/discuss.php?d=3537

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In how many ways can 5 similar balls be distributed in 3 different boxes? Ans: (by method given here) 21 But there is one basic question in you article (like in how many can one post 10 letters in 4 letter boxes: 4 * 4 *4.....10 times : 4^10....)..... So if we apply the above method considering similar letters and different letterboxes .....answer will come : 13C3 ? Have we considered all letters dissimilar to get 4^10? (can it be generalised where nothing is mentioned about similarity or dissimilarity ? ) Pls help ??????????? .... Naman S how parent | R eply

Re: Permutation and Combination by Siddha rth Kha nna - Sa turda y, 7 August 2010, 09:36 P M Hi T G Sir , ( in the se type s o f a rra nge m e nts

GB GB BG BG BG

Here every boy is sitting with one girl.... it the condition was "every boy wants to sit in-between 2 girls" then i would be a diff case altogether. If not then plz temme... y these cases are not to be considered... )

Eve n I ha ve the sa m e do ubt a s m e ntio ne d by nishcha i . C a nt we co nside r this a rra nge m e nt .

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Re: Permutation and Combination by ra vi ba ra nwa l - Sunda y, 8 August 2010, 03:32 AM a gre e wid siddha rth n nischa i. S how parent | R eply

Re: Permutation and Combination by k e sa v singh - W e dne sda y, 11 August 2010, 11:01 P M hi e ve ryo ne !

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions ca n a nybo dy he lp m e in be lo w que stio n? ho w m a ny diffe re nt sum s ca n be fo rm e d with the fo llo wing co ins 5 rupe e ,1 rupe e ,50 pa ise , 25 pa ise , 10 pa ise , 3 pa isa , 2 pa isa & 1 pa ise ? plz e le bo ra te S how parent | R eply

Re: Permutation and Combination by R a vi Ma thur - T ue sda y, 17 August 2010, 09:16 P M T he re a re 10 ste ps in a sta irca se a nd a pe rso n ha s to ta k e tho se ste ps. At e ve ry ste p the pe rso n ha s go t a cho ice o f ta k ing 1 ste p o r 2 ste ps o r 3 ste ps.T he num be r o f wa ys in whch pe rso n ca n ta k e tho se ste ps is?? C a n a nyo ne ple a se he lp m e with this sta irca se pro ble m . S how parent | R eply

Re: Permutation and Combination by ve rsha jhunjhunwa la - Sunda y, 29 August 2010, 12:05 AM O ut o f 21 tick e ts m a rk e d with num be rs fro m 1 to 21 ,thre e a re dra wn a t ra ndo m , find the pro ba bility tha t the thre e num be rs o n the m a re in A.P ca n u ple a se e x pla in the co m ple te m e tho d? S how parent | R eply

Re: Permutation and Combination by NIT IN NIGAM - T ue sda y, 31 August 2010, 07:57 AM Hi Ve rsha ...m y a ppro a ch is a s fo llo ws: fro m 1 to 21 find the no . o f AP 's tha t u ca n ge t a nd the re will be ca se s a cco rdingly: 1. AP with d = 1 , we ha ve 21 no s. Am o ng the se 21 no s. we ca n cho o se 3 no s. which a re in AP a s 1,2,3 o r 2,3,4 o r 3,4,5 a nd so o n...he nce to ta l no . o f ca se s will be 19 he re with la st ca se e nding a t 19,20,21 2. AP with d = 2, we ha ve two se rie s he re a ) 1,3,5,7......21 = 11 no s. he nce no s. ca n be cho se n a s 1,3,5 o r 3,5,7 a nd so o n ..so he re T O T AL C ASES = 9 b) 2,4,6,8......20 = 10 no s. he nce no s. ca n be cho se n a s 2,4,6 o r 4,6,8 a nd so o n..so he re T O T AL C ASES = 8 3. AP with d = 3, we ha ve the fo llo wing se rie s a ) 1,4,7,10,13,16,19 -> to ta l ca se s = 5 b) 2,5,8,11,14,17,20 -> to ta l ca se s = 5 c) 3,6,9,12,15,18,21 -> to ta l ca se s = 5 4. AP with d = 4, we ha ve the fo llo wing se rie s a ) 1,5,9,13,17,21 -> to ta l ca se s = 4 b) 2,6,10,14,18 -> to ta l ca se s = 3 c) 3,7,11,15,19 -> to ta l ca se s = 3 d) 4,8,12,16,20 -> to ta l ca se s = 3 5. AP with d = 5, we ha ve the fo llo wing se rie s a ) 1,6,11,16,21 -> T o ta l ca se s = 3 b) 2,7,12,17 -> T o ta l ca se s = 2 c) 3,8,13,18 -> T o ta l ca se s = 2 d) 4,9,14,19 -> T o ta l ca se s = 2 e ) 5,10,15,20 -> T o ta l ca se s = 2 6. AP with d = 6, we ha ve the fo llo wing se rie s a ) 1,7,13,19 -> T o ta l ca se s = 2 b) 2,8,14,20 -> T o ta l ca se s = 2 c) 3,9,15,21 -> T o ta l ca se s = 2 d) 4,10,16 -> T o ta l ca se s = 1 e ) 5,11,17 -> T o ta l ca se s = 1 f) 6,12,18 -> T o ta l ca se s = 1 7. AP with d = 7, we ha ve the fo llo wing se rie s a ) 1,8,15 -> T o ta l ca se s = 1 b) 2,9,16 -> T o ta l ca se s = 1 c) 3,10,17 -> T o ta l ca se s = 1 d) 4,11,18 -> T o ta l ca se s = 1 e ) 5,12,19 -> T o ta l ca se s = 1 f) 6,13,20 -> T o ta l ca se s = 1 g) 7,14,21 -> T o ta l ca se s = 1 8. AP with d = 8, we ha ve the fo llo wing se rie s a ) 1,9,17 -> T o ta l ca se s = 1 b) 2,10,18 -> T o ta l ca se s = 1 c) 3,11,19 -> T o ta l ca se s = 1 d) 4,12,20 -> T o ta l ca se s = 1 e ) 5,13,21 -> T o ta l ca se s = 1 9. AP with d = 9, we ha ve the fo llo wing se rie s a ) 1,10,19 -> T o ta l ca se s = 1 b) 2,11,20 -> T o ta l ca se s = 1

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions c) 3,12,21 -> T o ta l ca se s = 1 10 AP with d = 10, we ha ve the fo llo wing se rie s a ) 1,11,21 -> T o ta l ca se s = 1 no w to ta l no . o f AP 's ca se s tha t yo u ca n ha ve fro m the se no s. is 19+17+15+13+11+9+7+5+3+1 = 100 no w to ta l no . o f wa ys o f se le cting 3 no s. fro m give n 21 no s. a re 21C 3 = 1330 He nce the re quire d pro ba bility is 100/1330 I co uld no t think o f a sho rte r a ppro a ch but i ce rta inly fe e l tha t the re m ust be o ne ....T Gite s ple a se he lp he re ...k indly po st a sho rte r o r sim ple r a ppro a ch if yo u find o ne ...a nd le t m e k no w if the a nswe r is co rre ct... tha nk s Nitin S how parent | R eply

Re: Permutation and Combination by de e pti a na nd - Mo nda y, 6 Se pte m be r 2010, 08:50 P M hii...hv a que s..plz he lp m e o ut se t A is fo rm e d by se le cting so m e o f the num be rs fro m the first 100 na tura l num be rs such tha t the HC F o f a ny two num be rs in the se t a re sa m e Q 1:if e ve ry pa ir o f se t A ha s to be re a ltive ly prim e a nd se t A ha s m a x num be r o f e le m e nts po ssible ,the n in ho w m a ny wa ys se t A ca n be se le cte d..?? 1)64 2)96 3)72 4)108 Q 2: if the HC F o f a ny two num be rs in se t A is 3, the n wha t is the m a x im um no o f e le m e nts se t A ca n ha ve ..?? 1)10 2)12 3)11 4)14 S how parent | R eply

Re: Permutation and Combination by Anim e sh De va rshi - Sa turda y, 11 Se pte m be r 2010, 07:23 P M Hi , re g que stio n: ho w m a ny wa ys ca n fo r pe rso ns be se a te d o ut o f 5 bo ys a nd 3 girls o n fo ur diffe re nt se a ts? why ca n't we go fo r 8C 4? S how parent | R eply

Re: Permutation and Combination by ha rle e n m a nn - Mo nda y, 4 O cto be r 2010, 01:27 AM @de e pti a na nd Ans 1. think ing pa rt: he re , fo r e le m e nts to be m a x , it ca n be unde rsto o d tha t we ne e d to ta k e a ll prim e s num be rs = 0 & ca se a 1, a 2.. a r >= 1

the num be r o f so lutio ns a re = C (n-1, r-1) in

the re 's no uppe r lim it o n va ria ble o n le ft side he re . But what if there's an upper limit on variable like-

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MBA| CAT| CAT 2013| CAT 2014| CAT Online| MBA 2013| MBA 2014| MBA Entrance Exams| CAT Test| Preparation| CAT Questions Question: A dice is ro lle d 3 tim e s. W ha t a re the num be r o f wa ys in which the sum o f num be rs a ppe a ring o n the dice is 12? He re , le t the o utco m e s be a ,b a nd c. the re fo re , a + b+ c = 12, whe re 1