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Question

Let A and B be two sets such that n(A)=6 and n(B)=3, then number of onto functions from A to B is

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Solution

If n(A)=m and n(B)=n, where 1nm, then number of onto functions from A to B
=nr=1(1)nr nCrrm

Here, m=6,n=3
Number of onto functions
=3r=1(1)3r 3Crr6
= 3C1 3C2(26)+ 3C3(36)
=3192+729
=540

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