Question

Evaluate each expression.

$\frac{4!}{2!2!}$

Short answer

The value of the expression is $\frac{4!}{2!2!}=6$

Step-by-step solution

Step 1. Given Information.

Given to evaluate the expression $\frac{4!}{2!2!}$.

Step 2. Calculation.

$\begin{array}{l}\frac{4!}{2!2!}=\frac{4\cdot 3\cdot 2!}{2\cdot 1\cdot 2!}\\ \frac{4!}{2!2!}=\frac{4\cdot 3}{2\cdot 1}\\ \frac{4!}{2!2!}=\frac{12}{2}\\ \frac{4!}{2!2!}=6\end{array}$

Step 3. Conclusion.

Hence, the value of the expression is $\frac{4!}{2!2!}=6$.