Posted by: catindiaonline | October 25, 2008

Permutations and Combinations Basics

FUNDAMENTAL PRINCIPLE OF COUNTING

If an operation can be performed in ‘m’ different ways and another operation in ‘n’ different ways then these two operations can be performed one after the other in ‘mn’ ways.

If an operation can be performed in ‘m’ different ways and another operation in ‘n’ different ways then either ofthese two operations can be performed in ‘m+n’ ways.(provided only one has to be done)

This principle can be extended to any number of operations

FACTORIAL ‘n’

The continuous product of the first ‘n’ natural numbers is called factorial n and is deonoted by n! i.e, n!=1×2x3x…..x(n-1)xn.

PERMUTATION

An arrangement that can be formed by taking some or all of a finite set of things (or objects) is called a Permutation.

Order of the things is very important in case of permutation.

A permutation is said to be a Linear Permutation if the objects are arranged in a line. A linear permutation is simply called as a permutation.

A permutation is said to be a Circular Permutation if the objects are arranged in the form of a circle.

The number of (linear) permutations that can be formed by taking r things at a time from a set of n distinct things (r\underline<n) is denoted by ^n P_r \quad or \quad P(n,r).

^n P_r = n(n-1)(n-2)(n-3)......(n-r+1) = \frac{n!}{(n-r)!}.

For rest go to CAT India Online’s CATclub

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