Find the number of all onto functions from the set A = {1, 2, 3, ..., n} to itself.

Question:

Find the number of all onto functions from the set A = {1, 2, 3, ..., n} to itself.

Solution:

We know that every onto function from $A$ to itself is one-one.

So, the number of one-one functions $=$ number of bijections $=n !$

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