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

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.