this is my first post here
I'm studying for an exam and have problems with simplifying math problems including factorials.
Here is an example 1: $$ \frac{(n-3)!}{132} =10! \implies n=\ ? $$ apparently the answer is $15$ but i dunno the way?
another example 2: $$ \frac{(a-3)!}{x!} = 120 \implies \min(a+x)=\ ? $$ (answer is $8$)
Note that $132=11\times12$. So\begin{align}\frac{(n-3)!}{132}=10!&\iff(n-3)!=12\times11\times10!=12!\\&\iff n-3=12\\&\iff n=15.\end{align}Can you do the other one?