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

Question

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

Answer 1

Hello, thank you for taking the time to post your question!

In order to set this one up it wants you to take

Number of bowls = Number of cones / n!

For this one that becomes

Number of bowls = 3024 / 4! = 3024 / 24 = 126

Meaning that you can make 126 different 4-scoop ice cream bowls

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

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.