Chapter 11, Problem 12CR

To determine

To Find : The number of permutations.

Answer to Problem 12CR

The number of permutations of $36P2$ is $1260$

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 $36P2$

  $\begin{array}{l}36P2=\frac{36!}{\left(36-2\right)!}\text{ [use permutations formula]}\\ \text{ =}\frac{36!}{34!}\text{ [subtract]}\\ \text{ =}\frac{\mathrm{36.35.34}!}{34!}\text{ [Expand factorials and divide out common factors]}\\ \text{ = 36}\text{.35}=1260\text{ [multiply]}\end{array}$

The number of permutations of $36P2$ is $1260$