Chapter 11.8, Problem 7WE

To determine

To calculate:

The given factorial.

Answer to Problem 7WE

The solution of $\frac{10!}{7!3!}$ is $120$ .

Explanation of Solution

Given information:

Factorial:

  $\frac{10!}{7!3!}$

Calculation:

Consider the factorial $\frac{10!}{7!3!}$

So put the value $\frac{10!}{7!3!}$ into the formula $\frac{n!}{n!\cdot n!}$

  $\frac{n!}{n!\cdot n!}=\frac{10!}{7!3!}$

The factorial of $\frac{10!}{7!3!}$ is calculated as,

  $\begin{array}{l}\frac{10!}{7!3!}=\frac{10\times 9\times \mathrm{8.....}\times 1}{7\times 6\times 5\times \mathrm{.....1}\cdot 3\times 2\times 1}\\ =120\end{array}$

Thus, the solution of given factorial is $120$ .