Notes - Chapter 1 Combinatorial Analysis Permutations are...

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Chapter 1 – Combinatorial Analysis Permutations are arrangements of objects that are indistinguishable. The number of permutations of n objects is n!. The number of permutations of n objects take r at a time is ( 29 ! ! r n n P r n - = The number of permutations of n objects, of which n 1 are alike, n 2 are alike, …,n r are alike is ! ! ! ! 2 1 r n n n n The number of combinations of n objects taken r at a time is ( 29 ! ! ! r r n n r n C r n - = = * ; 1 0 = = n n n * = - r n r n n ; *(4.1) n r r n r n r n - + - - = 1 ; 1 1 1 The Binomial Theorem: (4.2): ( 29 = - = + n k k n k n y x k n y x 0 The number of possible divisions of n distinct objects into r distinct groups of respective sizes n 1 , n
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Notes - Chapter 1 Combinatorial Analysis Permutations are...

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