Six children are each offered a single scoop of any of 3 flavors of ice cream from the Combinatorial Creamery. In how many ways can each child choose a flavor for their scoop of ice cream so that each flavor of ice cream is selected by at least one child?
I don't think this question makes sense.
Each child can choose any of the three flavours.
The only time this is not true is if the child is the last or second last child to get a scoop and not all the flavours have been chosen yet.
Really, I do not think that the meaning of the question is discernible