5.4 - Math 1313 Section 5.4 Section 5.4 Permutations and...

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Math 1313 Section 5.4 1 Section 5.4: Permutations and Combinations Definition: n-Factorial For any natural number n, ݊ሺ݊ െ 1ሻሺ݊ െ 2ሻ … 3 ∙ 2 ∙ 1 0! = 1 A permutation is an arrangement of a specific set where the order in which the objects are arranged is important. Formula: ܲሺ݊, ݎሻ ൌ ௡! ሺ௡ି௥ሻ! , ݎ ൑ ݊ where n is the number of distinct objects and r is the number of distinct objects taken r at a time. Formula: Permutations of n objects, not all distinct Given a set of n objects in which ݊ objects are alike and of one kind, ݊ objects are alike and of another kind,…, and, finally, ݊ objects are alike and of yet another kind so that ݊ ൅ ݊ ൅ ⋯ ൅ ݊ ൌ ݊ then the number of permutations of these n objects taken n at a time is given by ݊! ݊ ! ݊ ! … ݊ ! A combination is an arrangement of a specific set where the order in which the objects are arranged is not important. Formula: ܥሺ݊, ݎሻ ൌ ௡! ௥!ሺ௡ି௥ሻ! , ݎ ൑ ݊ where n is the number of distinct objects and r is the number of distinct objects taken r at a time.