I have a problem with which I am struggling how to prove:
Let $A$ and $B$ be finite sets with $|A|\geq|B|$. How large is $|\{f:A\rightarrow B \mid \text{$f$ surjective} \}|$?
I already know that $\{f:A\rightarrow B \mid \text{$f$ is a function} \}=|B|^{|A|}=m^n$. But how do I go on from here?
