Advanced Mathematical Concepts - Precalculus with Applications chap13

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1、Chapter13Unit4DiscreteMathematics(Chapters12–14)CCOMBINATORICSOMBINATORICSAANDNDPPROBABILITYROBABILITYCHAPTEROBJECTIVES•Solveproblemsinvolvingcombinationsandpermutations.(Lessons13-1,13-2)•Distinguishbetweenindependentanddependenteventsandbetweenmutuallyexclusiveandmutuallyinclusiveevents.(Les

2、sons13-1,13-4,13-5)•Findprobabilities.(Lessons13-3,13-4,13-5,13-6)•Findoddsforthesuccessandfailureofanevent.(Lesson13-3)836Chapter13CombinatoricsandProbability13-1PermutationsandCombinationsOBJECTIVESalWorledREDUCATIONIvetteisafreshmanattheUniversityofMiami.Sheis•SolveproblemsrelatedtotheAplan

3、ningherfallschedulefornextyear.ShehasachoiceofthreepnBasicCountingplicatiomathematicscourses,twosciencecourses,andtwohumanitiescourses.Principle.Shecanonlyselectonecoursefromeacharea.Howmanycourse•Distinguishschedulesarepossible?betweendependentandindependentLetM,M,andMrepresentthethreemathcou

4、rses,SandSthescienceevents.12312courses,andHandHthehumanitiescourses.OnceIvettemakesaselection12•Solveproblemsfromthethreemathematicscoursesshehastwochoicesforhersciencecourse.involvingThen,shehastwochoicesforhumanities.Atreediagramisoftenusedtoshowpermutationsorallthechoices.combinations.3223

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212HMSHS11111M1H2M1S1H2HMSHS11212HMSH2122HMSHS12111M2H2M2S1H2HMSHS12212HMSH2222HMSHS13111M3H2M3S1H2HMSHS13212HMSH2322Ivettehas12possibleschedulesfromwhichtochoose.Thechoiceofselectingamathematicscoursedoesnotaffectthechoiceofwaystoselectascienceorhumanitiescourse.Thus,thesethreechoicesarec

6、alledindependentevents.Eventsthatdoaffecteachotherarecalleddependentevents.Anexampleofdependenteventswouldbetheorderinwhichrunnersfinisharace.Thefirstplacerunneraffectsthepossibilitiesforsecondplace,thesecondplacerunneraffectsthepossibilitiesforthirdplace,andsoon.Thebranchofmathematicsthatstud

7、iesdifferentpossibilitiesforthearrangementofobjectsiscalledcombinatorics.TheexampleofchoosingpossiblecourseschedulesillustratesaruleofcombinatoricsknownastheBasicCountingPrinciple.Lesson13-1PermutationsandCombinations837BasicSupposeonee