Tecnicas de Conteo

 

\CJRL]PJKFK \CJRL]PJKF K [L@CHDÐNJ@F KL UFCFOÆ   BF@\D[FK KL JCNLCJL]JF KL PJP[LOFP @HOU\[F@JHCFDLP DJ@LC@JF[\]F LC JCNLCJL]JF KL PJP[LOFP Z @HOU\[F@JÐC KLUF][FOLC[H KL @HOU\[F@JÐC Z PJO\DF@JÐC KL PJP[LOFP

LP[]\@[\]FP KJP@]L[FP UF]F DF @HOU\[F@JÐC

JCRLP[JNF@JHC #67 [Ê@CJ@FP KL @HC[LH

BF@JDJ[FKH]7 JCN. GF@V\LDJCL P. KL @AJCN Lstukjfctls7 Bdhrls, Ofrjf

1-:;5-6066

Pfofcjlnh, Dujs

1-:;=-66:=

Nruph7 6JD-6=;

Khojcnh 6= kl ofyh kld =56:

 

JCKJ@L

JC[]HK\@@JHC.......................................................................................................0 [L@CJ@FP KL @HC[LHP ................. .................. ................. ................. ......................................; .............................; Urjc`jpjh Buckfolctfd kld @hctlh........ Urjc`jpjh Oudtjpdj`ftjvh......... .................. .................. .................. ................. ................. .................. .................. .................. ................. ..........................................; ..................................;

Lglopdh Oudtjpdj`ftjvh.........................................................................................................................; Urjc`jpjh Fkjtjvh.....................................................................................................................................< .................. .................. ................. ................. .................. .................. .................. ................. ................. .................. ...........................................< ..................................< Lglopdh Fkjtjvh.........

¸Kðckl sl fpdj`f dfs [ê`cj`fs kl @hctlh lc df `hoputf`jðc8 ........................................................< ................. .................. ................. ................. .................. ..................... ..............................< ..................< Ulroutf`jðc y @homjcf`jðc........

Ulroutf`jðc............................................................................................................................................< ................. .................. ................. ................. .................. .................. .................. ................. ..............................................2 ......................................2 Lglopdh kl Ulroutf`jðc........

@homjcf`jhcls.......................................................................................................................................2 Lglopdh @homjcf`jðc.........................................................................................................................2 Kjblrlc`jf lctrl Ulroutf`jðc y @homjcf`jðc .....................................................................................> @HC@D\PJHC...........................................................................................................1 MJMDJHN]FBJF.........................................................................................................:

 

JC[]HK\@@JHC

Dfs tê`cj`fs kl `hctlh shc fqulddfs qul shc usfkfs pfrf lcuolrfr lvlcths kjbï`jdls kl `ufctjbj`fr. Dfs tê`cj`fs kl `hctlh pfrf lc`hctrfr ld c÷olrh kl frrlndhs phsjmdls kl hmglths lc uc `hcgucth h `hcgucths shc lslc`jfdls lc ld lstukjh kl df prhmfmjdjkfk. Df lcuolrf`jðc kl pucths oulstrfdls lc uc lspf`jh oulstrfd, lc h`fsjhcls ls kjbï`jd y dfmhrjhsf phr df `fctjkfk kl pucths f `hctfr h lcuolrfr, prhpj`jfckh qul sl pulkfc `holtlr lrrhrls fd loprlcklr lsf tfrlf. Lc lsths `fshs sl rl`urrl fd fcædjsjs `homjcfthrjh, qul ls ucf ofclrf oæs shbjstj`fkf kl `hctfr.

 

[L@CJ@FP KL @HC[LHP Dfs tê`cj`fs kl `hctlh shc ucf slrjl kl oêthkhs kl prhmfmjdjkfk tfomjêc `hch`jkf `hoh fcædjsjs `homjcfthrjh9 qul plrojtl kltlrojcfr ld c÷olrh phsjmdl kl rlsudtfkhs dðnj`hs qul `fml lsplrfr fd rlfdjzfr fdn÷c lxplrjolcth h lvlcth sjc cl`lsjkfk kl lcuolrfrdhs thkhs. Lstfs sl usfc `ufckh rlfdjzfr  dfs `ulctfs kl bhrof ofcufd sl `hcvjlrtl lc fdnh `hopdj`fkh `hopdj`fkh klmjkh f df nrfc `fctjkfk kl hmglths y/h vfrjfmdls.

Urjc`jpjh Buckfolctfd kld @hctlh Ld prjc`jpjh mæsj`h h buckfolctfd kl `hctlh ls pfrf kltlrojcfr dhs phsjmdls rlsudtfkhs `ufckh afy khs h oæs `frf`tlrïstj`fs qul pulklc vfrjfr. Pj uc lvlcth pulkl su`lklr h rlfdjzfrsl kl c ofclrfs kjblrlctls y sj, `hctjcufckh ld prh`lkjojlcth uc slnuckh lglopdh pulkl rlfdjzfrsl kl c6 ofclrfs kjblrlctls y fsï su`lsjvfolctl, lcthc`ls ld c÷olrh kl ofclrfs lc qul dhs lvlcths pulklc rlfdjzfrsl lc ld hrklc jckj`fkh ls ld prhku`th kl c6*c=*c0…

Urjc`jpjh Oudtjpdj`ftjvh Lstl prjc`jpjh lstfmdl`l qul, sj ucf hplrf`jðc sl pulkl af`lr kl  bhrofs y `fkf ucf kl lsfs bhrofs pulkl pu lkl ddl ddlvf vfrsl rsl f `fm `fmh h kl

 ofclrfs kjstjctfs lc ucf slnuckf hplrf`jðc, sl kj`l qul guctfs dfs



hplrf`jhcls pulklc ddlvfrsl f `fmh  x  bhrofs kjstjctfs.

Lglopdh Oudtjpdj`ftjvh Nfmrjldf usf kjstjctfs bhrofs kl pljcfrsl. Dhs `ufdls shc7 @fmlddh fofrrfkh, `fmlddh suldth, djzh, rjzh, hckudfkh y trlczfkh kurfctl dhs > kïfs kl df slofcf. ¸Kl `ufctfs bhrofs pulkl pljcfrsl Nfmrjldf kurfctl df slofcf8 Phdu`jðc7 Pl kfc 2 bhrofs kjstjctfs kl pljcfkhs, dh `ufd `fkf pljcfkh `hrrlsphckl f 6 kjf kl df slofcf. @7 2, df vfrjfmdl —@‟ `hrrlsphckl f dhs kj kjstjcths stjcths pljcfkhs P7 >, df vfrjfmdl —P‟ `hrrlsphckl f dhs kïfs kl df slofcf @*P? 2*>? ;= ‛-3 Nfmrjldf tjlcl ;= bhrofs kjstjctfs kl pljcfrsl kurfctl df slofcf.

 

Urjc`jpjh Fkjtjvh Lstl prjc`jpjh lstfmdl`l qul sj uc lvlcth sl pulkl ddlvfr f `fmh lc  h

 dunfrls kjstjcths, fkloæs kl



ch slr phsjmdl qul sl ddlvl f `fmh ld ojsoh lvlcth lc khs dunfrls kjstjcths fd ojsoh tjloph, lcthc`ls ld lvlcth sl pulkl rlfdjzfr kl (  + ) ofclrfs kjblrlctls.

Lglopdh Fkjtjvh  Fcthcjh qujlrl af`lr uc vjfgl plrh ch kl`jkl f `uæd klstjch9 lc df Fnlc`jf kl [urjsoh kld Pur dl hbrl`lc ucf prhoh`jðc pfrf vjfgfr f Clw Zhri h Dfs Rlnfs, ojlctrfs qul df Fnlc`jf kl [urjsoh kld Lstl dl rl`hojlckf vjfgfr f Brfc`jf, Jtfdjf h Lspföf. ¸@uæctfs fdtlrcftjvfs kl vjfgls kjblrlctls dl hbrl`lc Fcthcjh8 Phdu`jðc @hc df Fnlc`jf kl [urjsoh kld Pur Fcthcjh tjlcl = fdtlrcftjvfs (Clw Zhri h Dfs Rlnfs), ojlctrfs qul `hc df Fnlc`jf kl [urjsoh kld Lstl tjlcl 0 hp`jhcls (Brfc`jf, Jtfdjf h Lspföf). Ld c÷olrh kl fdtlrcftjvfs kjblrlctls ls7 C÷olrh kl fdtlrcftjvfs? o + c ? = + 0 ? < fdtlrcftjvfs.

¸Kðckl sl fpdj`f dfs [ê`cj`fs kl @hctlh lc df `hoputf`jðc8 Lc `hoputf`jðc ls cl`lsfrjh usfr dhs oêthkhs kl `hctlh pfrf `hctfr ld c÷olrh kl `j`dhs qul tjlcl uc prhnrfof, ld c÷olrh kl `hopfrf`jhcls qul rlfdjzf uc prhnrfof pfrf hrklcfr uc `hcgucth kl kfths, ld c÷olrh kl pfdfmrfs kjblrlctls tjlcl uc dlcnufgl `hc kltlrojcfkf nrfoætj`f, ld c÷olrh kl jctlr`fomjhs qul sl ddlvfc f `fmh lc uc prhnrfof pfrf rlshdvlr uc sjstlof kl l`uf`jhcls.

Ulroutf`jðc y @homjcf`jðc Ulroutf`jðc Dfs plroutf`jhcls shc ld c÷olrh kl bhrofs kjstjctfs lc qul uch h vfrjhs hmglths pulklc `hdh`frsl, jctlr`fomjfckh sus dunfrls y sjnujlckh `jlrtfs rlndfs lspl`ïbj`fs pfrf nufrkfr uc hrklc. [fomjêc sl pulkl `hcsjklrfr `hoh thkh frrlndh lc ld qul ls jophrtfctl df phsj`jðc qul h`upf `fkf uch kl dhs ldlolcths ldlol cths qul jctlnr jctlnrfc fc kj`ah frrlndh. Pu bðroud bðroudf f ls7 cUr? c!/(c c!/(c-r)!. -r)!. Khckl cUr shc dfs plrout plroutf`jhcl f`jhclss kld hmglth r, thofkhs lctrl c hmglths.

 

Lglopdh kl Ulroutf`jðc ¸Lc `uæctfs bhrofs sl pulklc sldl``jhcfr < plrshcfs kl lctrl uc nruph kl 1, sj ld hrklc kl sldl``jðc ls jophrtfctl8 Kfths7 C? 1 r? < CUr? C!/(C-r)! Phdu`jðc7

CUr ?1U< C!/(C-r)!? 1!/(1-