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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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What are C1, C2, and C3? – Paul Jan 10 '12 at 12:48
Combination. 5C1 .. – Q123 Jan 10 '12 at 12:59
up vote 3 down vote accepted

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

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