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$L e t X = \{a_{1}, a_{2}, . . . ., a_{6}\} a n d Y = \{b_{1}, b_{2}, b_{3}\} .$ The number of functions f from X to Y such that it is onto and there are exactly three elements x in X such that $f (x) = b_{1}$ is

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Correct option is D

Image b1 is assigned to any three of the six pre-images in C3 6 ways.Rest two images can be assigned to remaining three pre-images in 23-2 ways (as function is onto).Hence, number of functions are C3 6×23-2=20×6=120.

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Let X=a1,a2,....,a6 and Y=b1,b2,b3. The number of functions f from X to Y such that it is onto and there are exactly three elements x in X such that fx=b1 is

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$L e t X = \{a_{1}, a_{2}, . . . ., a_{6}\} a n d Y = \{b_{1}, b_{2}, b_{3}\} .$ The number of functions f from X to Y such that it is onto and there are exactly three elements x in X such that $f (x) = b_{1}$ is