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Question

# Let A={1,2,3,4,5,6} and B={a,b,c,d}, then the total number of possible functions from A to B

A
without any restriction is 64
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B
such that every element in B has atleast one pre-image is 1560
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C
such that all the elements in B should not have pre-image is 2536
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D
without any restriction is 46
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Solution

## The correct option is D without any restriction is 46Here, A={1,2,3,4,5,6} and B={a,b,c,d}, n=6, r=4 then the total number of possible functions from A to B is rn=46 ...(1) Total number of possible functions from A to B such that every element in B has atleast one pre-image is =rn−rC1(r−1)n+rC2(r−2)n+...+(−1)r−1⋅rCr−1(1)n =46−4C1(3)6+4C2(2)6−4C3(1)6=1560 ...(2) Total number of possible functions from A to B such that all the elements in B should not have pre-image =(1)−(2) 46−1560=2536

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