Six children are each offered a single scoop of any of 3 flavors of ice cream from the Combinations Creamery. 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?
+118680
Ways to be all the same flavour = 3
Ways exactly 5 can be the same = 6C5*3*2 = 36
Ways exactly 4 can be the same = 6C4*3*2*2 = 180
Ways exactly 3 can be the same = 6C3*3*2*2*2 = 480
Add them up = 699
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another thought...
How many ways altogther, no conditions 3^6 = 729
There are no ways to not double up the flavour, I mean they cannot all be differerent.
The only way NOT to have 3 or more of one flavour is for there to be 2 of each flavour.
6!/(2*2*2) = 90
729-90 = 639.
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If my logic was correct these 2 answers would be the same.
They are not the same so my logic is flawed.
MAYBE SOMEONE CAN POINT OUT THE LOGIC ERROR THAT I HAVE MADE. 
