Permutation & Combination

Introduction:

During the course of life, we stumble across situations were we are asked to arrange things. But we don’t have any idea that actually how many such arrangement are possible. This is where permutation and combination works. Also you guys might have seen number all around you like that in your recharge card, your bike’s number plate etc, all these arrangement are the result of permutation and combination. The concept of permutation and combination all starts  with the basics principle of counting and is explained below:

The Basic Principle of Counting

This principle can be stated as, “if one thing can be done in ‘m’ different ways and second thing can be done in ‘n’ different ways. Then the total numbers of ways in which both thing can be done is equal to m×n different ways for a finite set of elements.”

Now that fancy talks seem difficult, right? Let’s see what it says. Suppose we have to arrange 3 numbers, ‘1’,’2′,’3′ in 3 sheets of paper. Here we can place first number in any 3 sheet so first number has 3 choice i.e. first number can be arranged in 3 different ways. Again now for second number, since one place is take, there is 2 choice so can be arranged in 2 different ways and finally for last there is only one choice. Now according to basic principle of counting, total number of ways the numbers can be arranged is 3×2×1=6.

In tree diagram:

Fig: Tree diagram for showing ways to arrange 3 numbers.

Exercise:

1. A football stadium has four entrance gates and nine exists. In how many different ways can a man enter and leave the stadium?

           Solution:

           A man can enter in 4 ways and leave in 9 ways so, by basic principle of counting

           No. of ways a man can enter and leave the stadium is 4×9=36

[Because by basic principle of counting, if two different work can be done in ‘m’ and ‘n’ ways, they can be done together in m×n ways.]