Confusion in how to find number of onto functions if two sets are given

Asked May 27 '19 at 06:22

Active May 27 '19 at 09:27

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In the book it is given if A and B are two finite sets containing $m$ and $n$ elements, respectively, then the number of onto functions from A to B will be if

$n \leq m$

$$\sum_{r=1}^n (-1)^{(n-r)} {n \choose r}(r)^m $$

well I can't understand it and I am aware with combinations.

edited May 27 '19 at 09:27

N. F. Taussig

76,571

asked May 27 '19 at 06:22

Mad Dawg

1

Any attempt towards the solution? – Archis Welankar May 27 '19 at 06:34
1

See https://en.m.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle and search for Info functions. – Jens Schwaiger May 27 '19 at 06:40
Its inclusion-exclusion. – Wuestenfux May 27 '19 at 07:39
Of course "info functions" should read as "onto functions". – Jens Schwaiger May 28 '19 at 01:31

Confusion in how to find number of onto functions if two sets are given

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