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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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:
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online