Chapter 11.7, Problem 58S

To determine

The value of the expression $P\left(7,2\right)$ .

Answer to Problem 58S

  $42$

Explanation of Solution

Given:

The expression $P\left(7,2\right)$ .

Formula used:

  $\begin{array}{l}P\left(n,r\right)=P{}_r=\frac{n!}{\left(n-r\right)!}\\ \text{where,}\\ n!=n\times \left(n-1\right)\times \left(n-2\right)\times \mathrm{...}\times 3\times 2\times 1\end{array}$

Calculation:

In order to evaluate the value of the given expression, use the above permutation formula and simplify further as shown below,

  $\begin{array}{c}P\left(7,2\right)=P{}_2\\ =\frac{7}{\left(7-2\right)!}\\ =\frac{7!}{5!}\\ =\frac{7\cdot 6\cdot 5!}{5!}\\ =7\cdot 6\\ =42\end{array}$

Thus, the value of the expression is $42$.