How can I prove that the number of surjective mapping from the set $A$ to a set $B$ is $\sum\limits_{r=1}^n(-1)^{n-r} \binom{ n}{ r}r^m $, where $|A|=m$ and $|B|=n$.
I can't get any idea how to prove it. Is it possible to prove it?
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Make use of inclusion-exclusion. – Wuestenfux Sep 17 '18 at 13:32