Chapter 11, Problem 1RE

For Exercises 1-2, simplify the expression.

$\frac{8!}{3!\cdot 5!}$

To determine

To calculate: The simplification of the expression $\frac{8!}{3!\cdot 5!}$ .

Answer to Problem 1RE

The simplification of the given expression is 56.

Explanation of Solution

Calculation:

Consider the expression.

$\frac{8!}{3!\cdot 5!}$

For a positive integer $n$ , $n!=\left(n\right)\left(n-1\right)\left(n-2\right)\cdots \left(2\right)\left(1\right)$ .

So,

$\begin{array}{c}\frac{8!}{3!\cdot 5!}=\frac{8\cdot 7\cdot \stackrel{1}{\cancel{6}}\cdot \stackrel{1}{\cancel{5!}}}{\left(\cancel{3}\cdot \cancel{2}\cdot 1\right)\left(\cancel{5!}\right)}\\ =56\end{array}$

Hence, the simplification of the given expression is 56.