What is the number of injective maps from a set of cardinality $m$ into a set of cardinality $n$ $(m \leq n)$?
Number of Injective Maps
7
$\begingroup$
combinatorics
functions
-
4**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
-
0@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
-
0It is not very different in spirit from yours. Instead of posting, might as well upvote yours. – 2012-11-24