Let A ={1,2,3,...,m} and B={1,2,3,...,n}, where m>n. Find an expression for the number of function f : A--->B that are onto. Prove that the expression is correct.
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$\displaystyle \text{Surj}(m,n)=\sum\limits_{k=0}^{n} {(-1)^k \binom{n}{k}(n-k)^m} $
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