Question

Evaluate each expression.

$\frac{6!}{2!4!}$

Short answer

The value of the expression is $\frac{6!}{2!4!}=15$

Step-by-step solution

Step 1. Given Information.

Given to evaluate the expression $\frac{6!}{2!4!}$.

Step 2. Calculation.

$\begin{array}{l}\frac{6!}{2!4!}=\frac{6\cdot 5\cdot 4!}{2\cdot 1\cdot 4!}\\ \frac{6!}{2!4!}=\frac{6\cdot 5}{2\cdot 1}\\ \frac{6!}{2!4!}=\frac{30}{2}\\ \frac{6!}{2!4!}=15\end{array}$

Step 3. Conclusion.

Hence, the value of the expression is $\frac{6!}{2!4!}=15$.