A function f is called as onto function such that

f : A ->A if for every element x ∈ A then there exists y ∈ a such that f(x) = y.

The number of onto functions from a given set {1,2,3,..............,n} to itself is the permutation of n symbols 1,2,3,.....,n

So total number of onto functions from the set {1,2,3,.......,n} to itself = n!