Basic Principles Froblem-SoIvingCorner: Counting I ?J h _ d k I d??.E: Permutafiong and There s on 3; so many ands in a e: o car s.Combinations FRDM SHANEProblem-SoIvIngCorner: Combinations6.3 GeneralizedPermutations andCombinations6.4 Algorithms forGeneratillg In many di:+crctc problcrn.-+??., we arc conli?onlcLi with thc problcrn ofcounting_ For cJ-tatnplc,Perm tatF95 _ in Suction 4.3 wt: saw that in ordcr to ctstirnatc thc run tirnc oli an algori Lhrn, wt: nccdcdand CGm_bmat?Dn? to count I.hc nurnbcr ol? l.?tTl?tIJt-i- ccrtain stop}: or 1o-op:-; wcrc tJ.3t.L?.1?..2Llll.:l.l_ Counting alteo plays.TE?!- itmdCt:? tn Dficrete .1 crucial rolc in ?probability thcory. Bccau:-.?c of tho irnportancc ol? counting :1 r.?3.rictg,r ofT Pr_Dbab?hty _ _ uttctul aidtt, sornc quitc .~.?ophi:+ticatcLt, havc bcc.n dcvcltrpcd. In this chaptcr Wt.? dcvclop??.E?E Dficrete Pmhabmty scvcral tools for counting. Tl.?llLl?lL: 1.t.?.t.?l1t?ItI?.1t.tt.?.:?-l can bc l.t.?iL?.I?.l to Llcrivc lhc binomial thcorcrn.Thea: _ J Thc chaptcr concludcrt with adi .?iI?.:Lll-ll-l?tU1?t ol thc Pi gconholc Principlc, which oltcn allows.6?? E?øm?al COEHFCJEHE L1:-l lo provc thc cxi:-;tc11cc oi an objccl with ccrtain propcrtictt.and Combinatorialidentities6.3 The PigeonholePrinciple??.NotesChapter ReviewChapter Self-TestComputer Exercises6.1 -> Basic PrinciplesThc mcnu for Raft.? Quick Lunch is ti-l?ltJ-W1?l?ll1 Figurc 6.1.]. As you can hiI?.3L?.., it licaturctsC_.._gufl?I? 1?- F two appcti?.ccre__ thrcc main ClJILtl?til_?.!a?-, and Your bcvcragcs. How many dillcrcnt Ll?tl?lt?lL?.]?1-l-1? ? I?.?t.J1?l:?ih.?l oi onc rnain cou.n-?.c and onc bcvcragc?I?bc:-to :i:l:l.t.?tD11fi can b-I: ornittocl witJ1oLtt lottta of continuity.265??.
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