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Let $A$ and $B$ be sets with cardinalities m and n respectively where $m \ge n$ how many surjective functions are there from $A$ to $B$? Support your answer

I have no idea how to go about this one. Any help would be appreciated. Thanks in advance!

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  • This is probably what you're looking for: http://math.stackexchange.com/questions/500674/number-of-surjective-functions-from-a-to-b – Vikram Saraph Apr 07 '14 at 20:28

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See If $|A|=30$ and $|B|=20$, find the number of surjective functions $f:A \to B$. . A formula is given in terms of Stirling numbers of the second kind, for which there is no easy closed form formula with simple expressions but there are identities that let you compute it. But it's still a formula in terms of well-known quantities.

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