Chapter 11, Problem 11CR

To determine

To Find : The number of permutations.

Answer to Problem 11CR

The number of permutations of $8P6$ is $20160$

Explanation of Solution

Given information :

Consider the information provided in the question.

Formula used :

The number of permutation of $n$ objects taken $r$ at a time can be written as $n\mathrm{Pr}$ where,

  $n\mathrm{Pr}=\frac{n!}{\left(n-r\right)!}$

Calculation :

Use the formula provided above to find $8P6$

  $\begin{array}{l}8P6=\frac{8!}{\left(8-6\right)!}\text{ [use permutations formula]}\\ \text{ =}\frac{8!}{2!}\text{ [subtract]}\\ \text{ =}\frac{\mathrm{8.7.6.5.4.3.2.1}}{2.1}\text{ [Expand factorials and divide out common factors]}\\ \text{ = }\mathrm{8.7.6.5.4.3}=20160\text{ [multiply]}\end{array}$

The number of permutations of $8P6$ is $20160$