Question

Please select the best answer from the choices provided A B C D

Answer 1

ANSWER

C.
$\frac{1}{a(a - 1)}$

EXPLANATION

We want to simplify,

$\frac{(a - 2)!}{a!}$

Recall that,

$n!=n\times (n-1)\times (n-2)...2\times1$

We expand only the denominator until an equivalent expression for numerator shows up.

This implies that, the above expression is

$=\frac{(a - 2)!}{a(a - 1)(a - 2)!}$

We cancel out the common factors to get.

$=\frac{1}{a(a - 1)}$

Therefore the correct answer is option C.