Q. 103.8( 17 Votes )
Find the number of all onto functions from the set A = {1, 2, 3, …., n} to itself.
Answer :
TIP: –
Onto Function: – A function 
is said to be a onto function or surjection if every element of A i.e, if f(A) = B or range of f is the co – domain of f.
So, 
is Surjection iff for each 
, there exists 
such that f(a) = b
Now, f : A → A where A = {1, 2, 3,….,n}
All onto function
It’s a permutation of n symbols 1,2,3,….n
Thus,
Total number of Onto maps from A = {1, 2, 3, …., n} to itself =
Total number of permutations of n symbols 1,2,3,….n.
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