Chapter 11.8, Problem 5WE

To determine

To calculate:

The given factorial.

Answer to Problem 5WE

The solution of $\frac{100!}{99!}$ is $100$ .

Explanation of Solution

Given information:

Factorial:

  $\frac{100!}{99!}$

Calculation:

Consider the factorial $\frac{100!}{99!}$

So put the value $\frac{100!}{99!}$ into the formula $n!=n\left(n-1\right)!$

  $\frac{100!}{99!}=\frac{100\times 99!}{99!}$

The factorial of $\frac{100!}{99!}$ is calculated as,

  $\begin{array}{l}\frac{100!}{99!}=\frac{100\times 99!}{99!}\\ =100\end{array}$

Thus, the solution of given factorial is $100$ .