1313_section6o4 - Section 6.4 Permutations and Combinations...

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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 . Note: 0! = 1 Example: 2 1 . 2 ! 2 = = ; 120 1 . 2 . 3 . 4 . 5 ! 5 = = . Arrangements: n different objects can be arranged in ! n different ways. Example: In how many different ways can you arrange 4 different books on a shelf? Example: In how many ways can 5 people be seated? Arrangements 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 these objects can be arranged in: ! ! ! ! 2 1 r n n n n different ways. Example: In how many ways can you arrange 2 red, 4 blue and 5 black pencils? Example: How many 4 letter words can you form by arranging the letters of the word MATH? Example: How many 8 letter words can you form by arranging the letters of the word MINIMIZE?
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Section 6.4 – Permutations and Combinations 2 Definition: 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. Example: How many 2-digit numbers can be written by using the digits 1,2 and 3? (Repetition is not allowed) E= {1, 2, 3} List: 12, 13, 21, 23, 31, 32 6 1 6 ! 1 ! 3 )! 2 3 ( ! 3 ) 2 , 3 ( = = = - = P Example: A shelf has space for 4 books but you have 6 books. How many different
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This note was uploaded on 02/21/2012 for the course MATH 1313 taught by Professor Constante during the Spring '08 term at University of Houston.

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1313_section6o4 - Section 6.4 Permutations and Combinations...

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