30 CHAP

# 30 CHAP - 30. PERMUTATIONS AND COMBINATIONS IMPORTANT FACTS...

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30. PERMUTATIONS AND COMBINATIONS IMPORTANT FACTS AND FORMULAE Factorial Notation: Let n be a positive integer. Then, factorial n, denoted by n! is defined as: n! = n(n-1)(n-2). ....... 3.2.1. Examples: (i) 5! = (5x 4 x 3 x 2 x 1) = 120; (ii) 4! = (4x3x2x1) = 24 etc. We define, 0! = 1. Permutations: The different arrangements of a given number of things by taking some or all at a time, are called permutations. Ex. 1. All permutations (or arrangements) made with the letters a, b, c by taking two at a time are: (ab, ba, ac, bc, cb). Ex. 2. All permutations made with the letters a,b,c, taking all at a time are: (abc, acb, bca, cab, cba). Number of Permutations: Number of all permutations of n things, taken r at a time, given by: n P r = n(n-1)(n-2). ....(n-r+1) = n!/(n-r)! Examples: (i) 6 p 2 = (6x5) = 30. (ii) 7 p 3 = (7x6x5) = 210. Cor. Number of all permutations of n things, taken all at a time = n! An Important Result: If there are n objects of which p 1 are alike of one kind; p 2 are alike of another kind; p 3 are alike of third kind and so on and p r are alike of rth kind, such that (p 1 +p 2 +....... p r ) = n. Then, number of permutations of these n objects is:

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## This note was uploaded on 08/13/2011 for the course FSD 011 taught by Professor Vinh during the Spring '11 term at Beacon FL.

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30 CHAP - 30. PERMUTATIONS AND COMBINATIONS IMPORTANT FACTS...

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