Math1313-Section6.4-Blank - Section 6.4 Permutations and...

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Section 6.4 – Permutations and Combinations 1 Section 6.4 Permutations and Combinations Definition: n-Factorial For any natural number n, 1 2 3 ) 2 )( 1 ( ! = n n n n . 0! = 1 A permutation is an arrangement of a specific set where the order in which the objects are arranged is important. Formula: P ( n , r ) = )! ( ! r n n , r < n 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 1 n objects are alike and of one kind, 2 n objects are alike and of another kind,…, and, finally, r n objects are alike and of yet another kind so that n n n n r = + + + ... 2 1 then the number of permutations of these n objects taken n at a time is given by ! ! ! ! 2 1 r n n n n A combination is an arrangement of a specific set where the order in which the objects are arranged is not important. Formula: C ( n , r ) )! ( !

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