Question

Evaluate \(\frac{n!}{\left(n-r\right)!}\), when 
(i) n = 6, r = 2 (ii) n = 9, r = 5

Answer 1

(i) When n = 6, r = 2,

\(\frac{n!}{(n-r)!}=\frac{6!}{(6-2)!}\)

\(=\frac{6!}{4!}=\frac{6\times5\times4!}{4!}\)

\(=30\)

(ii) When n = 9, r = 5,

\(\frac{n!}{(n-r)!}=\frac{9!}{(9-5)!}\)

\(=\frac{9!}{4!}=\frac{9\times8\times7\times6\times5\times4!}{4!}\)

\(=9\times8\times7\times6\times5=15120\)