Probability (3-4) summary (counting)

Probability (3-4) summary (counting) - Permutation...

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Unformatted text preview: Permutation Permutation ) 1 ( ) 2 )( 1 ( +--- r n n n n Theorem The number of permutations of n distinct objects is n ! . In general, the number of permutations of n distinct objects taken r ≤ n at a time is )! ( ! r n n- = There are r terms n r P denoted by A-B-C-D D-A-B-C C-D-A-B B-C-D-A B-A-C-D D-B-A-C C-D-B-A A-C-D-B D-A-C-B B-D-A-C C-B-D-A A-C-B-D B-A-D-C D-B-C-A A-B-D-C C-B-A-D D-C-B-A A-D-C-B A-D-B-C C-A-D-B B-C-A-D C-A-B-D D-C-A-B B-D-C-A (Linear) Permutation of 4 distinct objects is 4!=24 A l l a r e d i f f e r e n t ! ! ! Circular permutation Circular permutation The number of different circular permutations of n distinct objects is (n-1)! A B C D D A B C C D A B B C D A Consider 4 distinct objects again A-B-C-D D-A-B-C C-D-A-B B-C-D-A Circular permutation A-B-C-D D-A-B-C C-D-A-B B-C-D-A In a circular setting, pattern A-B-C-D is “repeated” 4 times in the 4! ways. Similarly, other patterns are also “repeated” 4 times A-B-C-D D-A-B-C C-D-A-B B-C-D-A B-A-C-D D-B-A-C...
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This note was uploaded on 12/09/2010 for the course ENGLISH 1303 taught by Professor May during the Spring '10 term at HKU.

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Probability (3-4) summary (counting) - Permutation...

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