Chapter 13.2, Problem 66AYU

To determine

To find: The difference between the permutation and combination and an example to illustrate the explanation.

Answer to Problem 66AYU

The difference between the permutation and the combination with the example is illustrated.

Explanation of Solution

Consider the formula for the permutation is,

  $P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}$

Here, $n$ is the total number of objects and $r$ is the total number of objects selected.

Consider the formula for combination is,

  $C\left(n,r\right)=\frac{n!}{\left(n-r\right)n!}$

In permutation the arrangement of the number of selected items is important to obtain a new arrangement whereas in combination the arrangement of the selected items is irrelevant.

Consider the example, if two digits are selected by the use of A and B, then AB and BA are different, this is permutation.

If three teachers are selected the arrangement of the teachers is irrelevant and is known as the combination.