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Suppose $A = \{x,y,z,w\}$ and $B = \{1,2,3,4,5\}$. How many functions from $A$ to $B$ are not one-to-one?

I think the answer is $\binom 51+\binom 52+\binom 53$; is it right?

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    Combination. 5C1 ..2012-01-10

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It's the total number of functions minus the number that are 1-1: $5^4-5\cdot 4\cdot3\cdot2$.