Chapter 12.7, Problem 20E

To determine

To Find : The number of permutation of ${}_4{p}_2$

Answer to Problem 20E

The number of permutation of ${}_4{p}_2$ is 12.

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 ${}_8{p}_5$

  $\begin{array}{l}{}_n{p}_r=\frac{n!}{(n-r)!}\\ {}_4{p}_2=\frac{4!}{\left(4-2\right)!}\text{ [use permutation formula]}\\ =\frac{4\cdot 3\cdot 2!}{2!}\text{ [write as products and divide out common factors ]}\\ =\text{ 12 [multiply]}\end{array}$

The number of permutation of ${}_4{p}_2$ is 12