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What is the number of injective maps from a set of cardinality $m$ into a set of cardinality $n$ $(m \leq n)$?

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    **Choose** the range of the map. This can be done in $\binom{n}{m}$ ways. For any choice, there are $m!$ functions that have that range, for a total of $\binom{n}{m}m!$, none of the above.2012-11-24
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    @AndréNicolas This is a very clean way to think about the problem. I think it deserves to be posted as an answer.2012-11-24
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    It is not very different in spirit from yours. Instead of posting, might as well upvote yours.2012-11-24

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