Problem 65
Question
Solve by the method of your choice. 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?
Step-by-Step Solution
Verified Answer
2730 different ice cream cones can be created.
1Step 1: Flavor selection for the top scoop
The top scoop can be any of the 15 flavors available. So there are 15 different possibilities for the top scoop.
2Step 2: Flavor selection for the middle scoop
Since a different flavor must be selected for the middle scoop, and one flavor has already been used for the top scoop, there are 14 different possibilities.
3Step 3: Flavor selection for the bottom scoop
Similar to the previous step, need to choose a different flavor for the bottom scoop, means there are 13 different possibilities.
4Step 4: Applying the fundamental counting principle
After determining the different possibilities for each scoop, the number of different three flavor combinations can be found by multiplying the number of possibilities together: 15 options for the top scoop * 14 options for the middle scoop * 13 options for the bottom scoop = 2730 different three flavor combinations.
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