factorial negative

Question

I do not understand how the following simplification has been performed: $$\sum_{n=4}^7 \frac{n!}{(n-2)! (n-(n-2))!} = \sum_{n=4}^7 \frac{n(n-1)}{2!}$$

The problem I have is the "n-" in (n-(n-2))!

Could you please explain it to me stepwise ? Thanks

Answer 1

We have,

$(n-(n-2))!$

$=(n-n+2)!$

$=2!$