Q. 25 - Calculus

Question

Simplify the quotients in Exercises 21–28 without using a calculator.

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

Step-by-Step Solution

Answer

The value is $12.$

Step 1. Given information.

The given expression is $\frac{4!}{(2!)!}$.

Step 2. Value of the expression.

Now, we know,

$$\begin{gathered} n !=n(n-1) ! \\ Therefore, \\ \frac{4!}{(2!)!}=\frac{4!}{(2\times 1)!} \\ =\frac{4!}{2!} \\ =\frac{\left(4\right)\left(3\right)2!}{2!} \\ =12 \end{gathered}$$