+11 Six children are each offered a single scoop of any of 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 some flavor of ice cream is selected by exactly three children?
PS the other answer on the website 189 is wrong
-649 There are three ways to choose which flavor the three children will have. Once we have chosen the flavor, we can assign it to any three children in C(6,3)=20 ways (since we are selecting 3 out of 6 children). Now, we need to consider the remaining three children who will have different flavors.
There are 2 flavors that the remaining children can choose from, so there are 2×2×2=8 ways to choose the flavors for the remaining children.
So, the total number of ways to choose the flavors for all 6 children is 3×20×8=480.
