I have the following problem:
$$ N^n(N-n)!=A $$
Where $N$ and $A$ are constants. I want to solve this equation for $n$ (for a variation of the birthday problem), but I have little experience with combinatorics.
An approximate answer is acceptable, so I've tried using Stirling's approximation, but no matter how I manipulate it, I can't get an answer to fall out.
Any guidance would be appreciated.