Given:
n = 7, r =5
We are required to evaluate the expression:
[tex]\frac{n!}{(n-r)!r!}[/tex]Substituting we have:
[tex]=\text{ }\frac{7!}{(7-5)!5!}[/tex]Now let's simplify:
[tex]\begin{gathered} =\text{ }\frac{7\times6\times5!}{2!\times5!} \\ =\text{ 7 }\times\text{ 3} \\ =\text{ 21} \end{gathered}[/tex]Answer: 21
