# Q. 10 Find the number of all onto functions from the set $\{1, 2, 3, ... , n\}$ to itself.

The number of all onto functions from the set $\{1, 2, 3, ... , n\}$ to itself is  permutations on n symbols  1,2,3,4,5...............n.
Thus, total number of all onto maps from the set $\{1, 2, 3, ... , n\}$ to itself is same as  permutations on n symbols  1,2,3,4,5...............n which is  n.