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 two children?
Lets pretend that the 3 flavors are A, B, and C
how many ways can 2 children pick A? 6c2 = 15
How many ways can the leftover 2 of 4 children pick B? 4c2 = 6
How many ways can the last 2 pick B? 2c2 = 1
multiply that together you get 90