Chapter 10.5, Problem 9E

To determine

To calculate:

The solution of the expression

  $P{}_2$

Answer to Problem 9E

The solution of the expression $P{}_2$ is $20$ .

Explanation of Solution

Given information:

  $P{}_2$

Calculation:

The formula for permutation for $n$ objects taken $r$ at the time is as:

  $P{}_r=\frac{n!}{\left(n-r\right)!}\cdot \cdot \cdot \left(1\right)$

Where,

  $\begin{array}{l}n=5\\ r=2\end{array}$

Put the values in equation (1)

  $\begin{array}{l}P{}_2=\frac{5!}{\left(5-2\right)!}\\ P{}_2=\frac{5!}{3!}\\ P{}_2=\frac{5\times 4\times 3\times 2\times 1}{3\times 2\times 1}\\ P{}_2=20\end{array}$

Hence, the solution of the expression $P{}_2$ is $20$ .