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Let X={a1, a2, ,a6}a n dY={b1, b2,b3}dot...

Let `X={a_1, a_2, ,a_6}a n dY={b_1, b_2,b_3}dot` The number of functions `f` from `xtoy` such that it is onto and there are exactly three elements `xinX` such that `f(x)=b_1` is 75 (b) 90 (c) 100 (d) 120

A

75

B

90

C

100

D

120

Text Solution

Verified by Experts

The correct Answer is:
D
Image `b_(1)` is assigned to any three of the six pre-images in `""^(6)C_(3)` ways.
Rest two images can be assigned to remaining three pre-images in `2^(3)-2` ways (as function is onto).
Hence, number of function are `""^(6)C_(3) xx (2^(3)-2)=20xx6=120.`
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