Question

find the value of \\(\frac{8!}{5!3!}\\).

Explanation:

Step1: Expand factorials

$$\begin{align*} \frac{8!}{5!3!}&=\frac{8\times7\times6\times5!}{5!\times3!}\\ \end{align*}$$

Cancel out \(5!\) in numerator and denominator.

Step2: Calculate \(3!\)

Since \(3!=3\times2\times 1 = 6\), then \(\frac{8\times7\times6}{6}\)
Cancel out \(6\) in numerator and denominator.

Step3: Multiply remaining numbers

\(8\times7=56\)

Answer:

\(56\)