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Find no of all onto function from set A=(1,2,3,4,............n) to itself

Find no of all onto function from set A=(1,2,3,4,............n) to itself

Grade:12

1 Answers

Vikas TU
14149 Points
3 years ago
Dear Student,
since f is onto, all elements have unique preimage .
        1 à n
        2 à n-1
        3à n-2 …….
…     |
        |
        n à 1
Total no. Of onto functions = n×(n-1)…..(2)(1)
                                                    = n! 
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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