Combinación y Permutación en Matematicas y Estadistica
November 16, 2022 | Author: Anonymous | Category: N/A
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]HBB@[ M@ CH]@CH]DFHV- FLCKDGHFDÖG T U@[CP]HFDÖG
[HJH@B N@[GHG ]HB@[L HBZH[HML
MLF@G]@ FHCDBL AH[_LG
JPGMHFDÖG PGDZ@[VD]H[DH M@ VHG ADB PGDVHGADB JHFPB]HM M@ FD@GFDHV @FLGÖCDFHV T HMCDGDV][H]DZHV HMCDGDV][HFDÖG M@ @CU[@VHV V@M@ TLUHB ;5;8
[`slbv`r bls sdaud`gt`s `o`rfdfdls 8. @muhrml, Fhrbls y V`radl s` nhg pr`s`gthml h ug flgfursl m` pdgturh. @b flgfursl ltlrah $;55 hb prdc`r buahr y $855 $855 hb s`augml. ¼M` ¼M` fuègths jlrch jlrchss s` pu`m` pu`m`gg r`phrtdr bls pr`cdls m` prdc`r y s`augml buahr< !
3
( ) !
∑∑
!
∛)! 3 3 (∛)
3 3 :
!
;. Pg fn`j vh h pr`phrhr ugh `gshbhmh m` v`rmurhs flg tlcht`, zhghnlrdh, phph y kröflbd. ¼M` fuègths jlrchs s` pu`m` pr`phrhr bh `gshbhmh ushgml slbl ; dgar`md`gt`s< 3 3
! ( )! ! =! (= ;)! ;!
3
=∑6∑;∑8 ;! ∑ ;!
3
;= ;∑;
3
;= =
3 : . .
6. V` vh h prlarhchr ug tlrg`l m` ho`mr`z phrh bls 85 dgt`arhgt`s m` ug fbuk. ¼Fuègtls phrtdmls s` m`k`g prlarhchr sd fhmh dgt`arhgt` ouahrè flg fhmh ugl m` bls m`cès sdg phrtdmls m` r`vhgfnh< 3
! ( )! !
3
85!
3
85!
85∑4∑>!
3
8 5 ∑ 4 ∑ >!
(8 5 ;)! ;! > ! ; ! > ! ∑ ; ∑ 8 >!∑; ∑ 8 3 =0
30∑4
=. Flgsdm`rh ug arupl m` 85 `stumdhgt`s m` bls fuhb`s = slg cuo`r`s y : slg nlckr`s. M` hfu`rml flg `sh dgjlrchfdög, m`t`rcdg`? h) @b gÿc`rl m` jlrchs `g qu` s` pu`m` `b`adr ug r`pr`s`gthgt` m`b arupl. 3
! ( )! !
3
85! (8 5 8) 8)! 8!
3
85 ∑ 4! 4! 8!
3
85 8
3 85
k) @b gÿc`rl m` jlrchs `g qu` s` pu`m` `b`adr ug fl flcdtä cdtä m` 6 cd`ckrls, cd`ckrls, mlgm` hb c`gl c`glss ugl m` bls cd`ckrls s`h cuo`r. - Vd `b flcdtä `stè jlrchml plr 8 cuo`r, sdagdjdfh qu` m` bhs = cuo`r`s s`b`ffdlghr`cls ugh, y m` bls : nlckr`s s`b`ffdlghr`cls ;. 3
=! (= 8)! 8!
:! (: ;)! ;!
3
= 6! 6! 8! 8!
: 0 =! =! ; 8
3 = 80 80 3 :5
- Vd `b flcdtä `stè jlrchml plr ; cuo`r, sdagdjdfh qu` m` bhs = cuo`r`s s`b`ffdlghr`cls ;, y m` bls :
nlckr`s s`b`ffdlghr`cls 8. 3
=! (= ;)! 8!
:! (: 8)! 8!
3
= 6 ;! ;! ; 8! 8!
: 0! 0! 8
3 : : 3 6:
- Vd `b flcdtä `stè jlrchml plr 6 cuo`r`s, sdagdjdfh qu` m` bhs = cuo`r`s s`b`ffdlghr`cls 6, y m`
bls : nlckr`s gl s`b`ffdlghr`cls h gdgaugl.
3 (
! ∛)!! ∛)
! (∛ ∛))!!
3
!
! !
! !
3 = 8 3 =
@g tlthb t`g`cls qu` :5 + 6= + = 3 855 jlrchs s` pu`m` `b`adr ug flcdtä m`6 cd`ckrls, mlgm` hb c`gls ugl m` bls cd`ckrls s`h cuo`r. 0. ¼Fuègtls gÿc`rls m` 6 fdjrhs mdstdgths s` pu`m`g jlrchr flg bls gÿc`rls ;, 6, 0, 1, >, 4< !
3
( )! 3
:! (: 6)!
3 8;5
:. Fdgfl p`rslghs `gtrhg `gtrhg `g ug vhaög m` j`rrlfhrrdb j`rrlfhrrdb `g qu` nhy 1 hsd`gtls. ¼M` fuègths chg`rhs mdstdgths pu`m`g s`gthrs`< 3 3
!
( )! 1!
(1 0)!
3 ;0;5
1. ¼Fuègtls gÿc`rls m` = fdjrhs mdstdgths s` pu`m`g jlrchr flg bls gÿc`rls 8, 6, 0, :, >, 5< ¼Fuègtls m` `bbls slg phr`s< 3 3
3
! ( ) !
:! (: =)! 0! (0 6)!
3
!
( )!
3 6:5
3 :5
6:5 :5 3 655 3 3
! ( ) !
3
!
( )!
0!
3 :5 (0 6)! 0! 3 3 :5 (0 6)! :5 + :5 3 8;5
>. Vd t`g`cls bh sdaud`gt` pbhfh m` hutl, flg? h. ; b`trhs y 6 gÿc`rls, m` bhs fuh fuhb`s b`s s` pu`m`g r`p`tdr. ¼Fu ¼Fuègths ègths pht`gt`s s` pu`m`g pu`m`g jlrchr< Flgsdm`r` flcl ;1 `b gÿc`rl m` b`trhs m`b hk`f`mhrdl.) ;1 85 3 1;45 1;4555 55
k. 6 b`trhs y = gÿc`rls, m` bhs fuhb`s s` ppu`m`g u`m`g r`p`tdr. ¼Fu ¼Fuègths ègths pht`gt`s s` pu`m`g jlrchr< jlrchr< Flgsdm`r` flcl ;1 `b gÿc`rl m` b`trhs m`b hk`f`mhrdl.) ;1 85 3 84 84:>6 :>6555 5555 5
4.
h) ¼Fuègths gÿc`rls mdstdgtls pu`m`g jlrchrs` tlchgml fuhtrl mãadtls 6, =, 1, 0, >, 8, sdg r`p`tdfdög< :
0
=
6
k) ¼Fuègths flckdghfdlg`s flckdghfdlg`s mmdstdgths dstdgths pu`m`g jlrchrs` tlchgml fuhtrl mãadtls 6, =, 11,, 0, >, 8< 3
! ( )! !
3
:! (: =)! =!
3
: 0 = 6 ;! 8 ;! 8
3 6:5
85. V` m`s`h jlrch jlrchrr ugh flcdsdög m` 0 hbucgls, 6 mm`` prdc`r høl y ; m` s`augml hhøl. øl. Vd s` pr`s`gthg 1 vlbugthrdls m` prdc`rl p`rl slbl 6 m` s`augml. s`augml. ¼M` fuègths chg` chg`rhs rhs pu`m` jlrchrs` `sth flcdsdög< flcdsdög< 3
! (∛) ∛)!!
! (∛) ∛)!!
3 850 Chg`rhs s` pu`m` jlrchr bh flcdsdög.
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