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

Answers (1)

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.

 Hence, permutations  on n symbols  1,2,3,4,5...............n = 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.

 

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