Permutations

Permutations:

Introduction:

Let us understand the meaning of the term Permutation with the help of few examples.In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging in an ordered fashion) objects or values.Informally, a permutation of a set of values is an arrangement of those values into a particular order. Thus there are six permutations of the set {1,2,3}, namely [1,2,3], [1,3,2], [2,1,3], [2,3,1], [3,1,2], and [3,2,1].
The different arrangements that can be made with a given number of things taking some or all of them at a time are called permutations.

The symbol nPr or P(n,r) is used to denote the number of permutations of n things taken r at a time.

Examples:


1. 2 and 3 are two digits and with these digits, the numbers 32 and 23 are formed. Although both numbers viz., 32 and 23 consist of the digits 2 and 3, the order of digits is different. Each of the above arrangements is called a 'permutation'. Thus, the number of arrangements or permutations of two distinct digits 2 and 3 is 2.
2. The permutation of the three letters a, b, c taken two at a time are ab,ba,ac,bc,cb.(6 in number)

Question: Find the number of permutations of the elements in the set {1, 3, 5, 7, 9, 11}.

A ) 6
B ) 21
C ) 36
D ) 720

Steps to derive

1 Number of elements in the set = 6

2 Number of permutations of 6 distinct elements of the set is 6P6.
[nPn = n!.]
3 = 6!

4 = 6 · 5 · 4 · 3 · 2 · 1

5 = 720

Hope you like the above example of Permutations.Please leave your comments, if you have any doubts.