Chapter 11, Problem 10CR

To determine

To Find : The number of permutations.

Answer to Problem 10CR

The number of permutations of $11P3$ is $\text{990 }$

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 $11P3$

  $\begin{array}{l}11P3=\frac{11!}{\left(11-3\right)!}\text{ [use permutations formula]}\\ \text{ =}\frac{11!}{8!}\text{ [subtract]}\\ \text{ =}\frac{\mathrm{11.10.9.8.7.6.5.4.3.2.1}}{\mathrm{8.7.6.5.4.3.2.1}}\text{ [Expand factorials and divide out common factors]}\\ \text{ = 11}\text{.10}\text{.9 = 990 [multiply]}\end{array}$

The number of permutations of $11P3$ is $\text{990 }$