Chapter 11.8, Problem 10WE

To determine

To calculate:

The given expression.

Answer to Problem 10WE

The answer of expression $\frac{n}{\left(n-2\right)!}$ is $n\left(n-1\right)$ .

Explanation of Solution

Given information:

Expression:

  $\frac{n}{\left(n-2\right)!}$

Formula used:

Factorial rule,

  $\frac{n}{\left(n-m\right)!}=n\cdot \left(n-1\right)\mathrm{....}\left(n-m+1\right),n>m$

Calculation:

Consider expression $\frac{n}{\left(n-2\right)!}$

Now cancel the factorials $\frac{n}{\left(n-m\right)!}=n\cdot \left(n-1\right)\mathrm{....}\left(n-m+1\right)$

  $\begin{array}{l}\frac{n}{\left(n-2\right)!}=n\left(n-1\right)\\ =n\left(n-1\right)\end{array}$

Hence, the answer is $n\left(n-1\right)$ .