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

 Aug 4, 2023

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​.

 Aug 4, 2023

4 Online Users