Question: simplify $$\frac{(n-1)!}{(n-2)!}$$
What I did was:
$$\frac{(n – 1)!}{(n – 2)! \times (n – 3)!}$$
This I did following the rule $n! = n \times (n – 1)!$.
But my answer just doesn't look correct and I don't have a solution guide that tells me the correct answer. This is why I don't know whether my answer is correct or not.
Best Answer
Note that $(n-1)! = \color{blue}{(n-1)}(n-2)\cdots (2)(1) = \color{blue}{(n-1)}(n-2)!$ by plugging in $(n-2)! = (n-2)\cdots (2)(1)$ into the expression for $(n-1)!$.
So $$\frac{(n-1)!}{(n-2)!} = \frac{(n-1)(n-2)!}{(n-2)!} = n-1$$