## Wednesday, November 25, 2009

### permutation & combination

Definition:

Permutation:
An arrangement is called a Permutation. It is the rearrangement of objects or symbols into distinguishable sequences. When we set things in order, we say we have made an arrangement. When we change the order, we say we have changed the arrangement. So each of the arrangement that can be made by taking some or all of a number of things is known as Permutation.

Combination:
A Combination is a selection of some or all of a number of different objects. It is an un-ordered collection of unique sizes.In a permutation the order of occurence of the objects or the arrangement is important but in combination the order of occurence of the objects is not important.

Formula:

Permutation = nPr = n! / (n-r)!
Combination = nCr = nPr / r!
where,
n, r are non negative integers and r<=n.
r is the size of each permutation.
n is the size of the set from which elements are permuted.
! is the factorial operator.

Example:Find the number of permutations and combinations: n=6; r=4.

Step 1: Find the factorial of 6.
6! = 6×5×4×3×2×1 = 720

Step 2: Find the factorial of 6-4.
(6-4)! = 2! = 2

Step 3: Divide 720 by 2.
Permutation = 720/2 = 360

Step 4: Find the factorial of 4.
4! = 4×3×2×1 = 24

Step 5:Divide 360 by 24.
Combination = 360/24 = 15