Probability (3-4) summary (counting)

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

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Permutation

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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 All are different!!!

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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

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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 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

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