Find the number of all onto functions from the set {1, 2, 3, … , n) to itself.

Onto functions from the set $\{1,2,3, \ldots, n\}$ to itself is simply a permutation on $n$ symbols $1,2, \ldots, n$.

Thus, the total number of onto maps from $\{1,2, \ldots, n\}$ to itself is the same as the total number of permutations on $n$ symbols $1,2, \ldots, n$, which is $n !$.