Chapter 11, Problem 9CR

To determine

To Find : The number of permutations.

Answer to Problem 9CR

The number of permutations of $9P2$ is $\text{72}$

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 $9P2$

  $\begin{array}{l}9P2=\frac{9!}{\left(9-2\right)!}\text{ [use permutations formula]}\\ \text{ =}\frac{9!}{7!}\text{ [subtract]}\\ \text{ =}\frac{\mathrm{9.8.7.6.5.4.3.1}}{\mathrm{7.6.5.4.3.2.1}}\text{ [Expand factorials and divide out common factors]}\\ \text{ = 9}\text{.8 = 72 [multiply]}\end{array}$

The number of permutations of $9P2$ is $\text{72}$