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Chapter 11: Problem 49

Using 15 flavors of ice cream, how many cones with three different flavors can you create if it is important to you which flavor goes on the top, middle, and bottom?

Short Answer

Expert verified
The answer is 2730 unique three flavor ice cream cones could be created.

Step by step solution

01

- Determine the number of choices for the top flavor

For the top scoop, there are 15 different flavors to choose from, hence 15 choices.
02

- Determine the number of choices for the middle flavor

After choosing the first flavor, there will be 14 remaining flavors to choose from for the middle placement. So, there are 14 choices for the middle scoop.
03

- Determine the number of choices for the bottom flavor

Finally, after choosing two different flavors, there will be 13 flavors left for the bottom scoop. Therefore, there are 13 choices for the bottom flavor.
04

- Calculate the number of permutations

The total number of permutations can be calculated by multiplying the number of choices for each scoop. This would be \(15 \times 14 \times 13\).

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