Question

Find the indicated expression, where n = 7, r = 5. (Simplify the answer as much as possible.)n!/(n-r)!r!

Answer 1

Given:

n = 7, r =5

We are required to evaluate the expression:

$\frac{n!}{(n-r)!r!}$

Substituting we have:

$=\text{ }\frac{7!}{(7-5)!5!}$

Now let's simplify:

$\begin{gathered} =\text{ }\frac{7\times6\times5!}{2!\times5!} \\ =\text{ 7 }\times\text{ 3} \\ =\text{ 21} \end{gathered}$

Answer: 21