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Question

If A={1,2,3,4} and B={5,7,9}, then the number of onto function from A to B is

A
36
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B
45
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C
81
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D
64
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Solution

The correct option is A 36
If the set A has n elements and set B has r elements, then the number of onto function from set A to set B is equivalent to distributing n distinct objects into r distinct boxes such that each box gets at least one object.

Total number of onto functions =rn rC1(r1)n+ rC2(r2)n......

Here, n=4 & r=3
=34 3C1(31)4+ 3C2(32)4=8148+3=36

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