:Anorderedr-selectionfromasetS(“traditional”name:r-permutation):Thenumberoforderedr-selectionsisdenotedP(n,r)inmanyundergraduateleveltextbooks,perpetuatingtheerainwhichitwasdifficulttotypesetitsvalue,whichisDEF:Anunorderedr-selectionfromasetS(“traditional”name:bination):Thenumberofunorderedr-selectionsisdenotedC(n,r)inmanyundergraduateleveltextbooks,perpetuatingtheerainwhichitwasdifficulttotypesetthebinomialcoefficientDISAMBIGUATION::Orderedselectionswereintroducedasamathematicalmodelforthenumberofdifferentpossible5-cardsequencesfroma52-:Supposethereare7flags,?(n,r)=.Thatis,thenumberoforderedselectionsofritems(withoutrepetition)fromasetofnitemsequalsProof:Byinductiononr,?ANSWER::Letbethesetofallorderedr-
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