Find the number of all onto functions from the set {1, 2, 3, , n) to itself - Maths - Relations and Functions

Question

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

Gopal Mohanty · Accepted Answer

Onto functions from the set {1, 2, 3, … ,n} to
itself is simply a permutation on 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

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