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Question
Find the number of all onto functions from the set {1, 2, 3, ..., n} to itself.
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Solution
Onto functions from the set {1, 2, 3, ..., n} to itself are simply permutations on the n symbols 1, 2, ..., n.
Thus, the total number of onto maps from {1, 2, ..., n} to itself is the same as the total number of permutations on n symbols 1, 2, ..., n, which is n!.
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