ANSWER
C.
[tex] \frac{1}{a(a - 1)} [/tex]
EXPLANATION
We want to simplify,
[tex] \frac{(a - 2)!}{a!} [/tex]
Recall that,
[tex]n!=n\times (n-1)\times (n-2)...2\times1[/tex]
We expand only the denominator until an equivalent expression for numerator shows up.
This implies that, the above expression is
[tex]=\frac{(a - 2)!}{a(a - 1)(a - 2)!} [/tex]
We cancel out the common factors to get.
[tex]=\frac{1}{a(a - 1)} [/tex]
Therefore the correct answer is option C.
