Permutation and Combination

 In the previous post we have discussed about parametric equation and In today's session we are going to discuss about Permutation and Combination.

Collection of different objects and symbols in a particular sequence or particular order is known as permutation.

Collection of different objects is called as combination here order doesn't matters. In other words it is an unordered collection of a unique size.

Now we will talk about the formula for finding the Permutation and Combination. 

Formula to find the permutation is given as:

Permutation = ⁿp_r = n! / (n – r)!,

And formula to find the combination is given as:

Combination = ⁿC_r = ⁿp_r / r!;

Here, value of ‘n’ and ‘r’ indicate the non- negative integers and also r ≤ n value.

Value of ‘r’ indicates the size of each permutation.

Value of ‘n’ indicates the size of set from which element are permuted.

‘!’ indicate the factorial operator.

Now we will see example of combination and permutation.

Example: Calculate the number of permutation and combination where value of ‘n’ is 7 and the value of ‘r’ is 4?

Solution: We know that formula for permutation and combination is:

Permutation = ⁿp_r = n! / (n – r)!,

Combination = ⁿC_r = ⁿp_r / r!;

Given, n = 7 and r = 4.

First we will find the factorial of 7. The factorial of 8 is = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040.

Now find the factorial of (7 – 4);

The factorial of (7 – 4) is = (7 – 4)! = 3!,

So the factorial of 3 is = 3 * 2 * 1 = 6;

Now divide 5040 by 6;

Permutation = 5040 / 6 = 840;

Now find the factorial of 4.

The factorial of 4 is = 4 * 3 * 2 * 1 = 24;

Now divide 840 by 24.

Combination = 840 / 24 = 35.

We will see How to Find the Volume of a Cube in the next session.

Cbse class 12 board papers can be downloaded from CBSE board website.