3024 different 4-scoop ice cream cones. How many different 4-scoop bowls can you make.

## 3024 different 4-scoop ice cream cones. How many different 4-scoop bowls can you make.

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# 1 Answer

If we assume the position of each scoop in the stacked cone of 4 scoops matters, but its position in the bowl does not, this reduces to a problem of permutation vs. combination. For every combination of 4 scoops, they can be arranged in 4! = 4*3*2*1 = 24 ways. So we need to divide 3024 by 24 to get the number of 4-scoop combinations that are possible. 3024/24 = 126 different bowls.