Question

Evaluate each expression.

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

Short answer

The value of the expression is $\frac{8!}{3!5!}=56$

Step-by-step solution

Step 1. Given Information.

Given to evaluate the expression $\frac{8!}{3!5!}$.

Step 2. Calculation.

$\begin{array}{l}\frac{8!}{3!5!}=\frac{8\cdot 7\cdot 6\cdot 5!}{3\cdot 2\cdot 1\cdot 5!}\\ \frac{8!}{3!5!}=\frac{8\cdot 7\cdot 6}{3\cdot 2\cdot 1}\\ \frac{8!}{3!5!}=\frac{8\cdot 7\cdot 6}{6}\\ \frac{8!}{3!5!}=56\end{array}$

Step 3. Conclusion.

Hence, the value of the expression is $\frac{8!}{3!5!}=56$.