Chapter 12.7, Problem 21E

To determine

To Find : The number of permutation of ${}_8{p}_5$

Answer to Problem 21E

The number of permutation of ${}_8{p}_5$ is 6720.

Explanation of Solution

Given information :

Consider the information provided in the question.

Formula used :

  ${}_n{p}_r=\frac{n!}{(n-r)!}$

Calculation :

Use the formula provided above to find ${}_8{p}_5$

  $\begin{array}{l}{}_n{p}_r=\frac{n!}{(n-r)!}\\ {}_8{p}_5=\frac{8!}{\left(8-5\right)!}\text{ [use permutation formula]}\\ =\frac{8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3!}{3!}\text{ [write as products and divide out common factors ]}\\ =\text{ 6720 [multiply]}\end{array}$

The number of permutation of ${}_8{p}_5$ is 6720