Question

Laura wants 3 scoops of ice cream. She can choose from vanilla, chocolate, mint, raspberry, blueberry, and coffee flavors. How many combinations of 3 scoops of ice cream can Laura choose from? Show your work and explain whether or not this is a scenario in which repetition is allowed.

Answer 1

Laura can choose from 20 different combinations of 3 scoops of ice cream from the 6 flavors available, without allowing for repetition of flavors.

Step-by-step explanation:

Laura wants to choose 3 scoops of ice cream from 6 different flavors: vanilla, chocolate, mint, raspberry, blueberry, and coffee. Since the question doesn't allow flavor repetition, she is forming combinations without repetition. To calculate the number of different combinations she can have, you'd use the combination formula for selecting r items (which in this case is 3 scoops) from n items (which is 6 flavors), without repetition, which is nCr = n! / (r! (n-r)!).

The calculation is therefore:

1. 6! / (3! * (6-3)!) = 720 / (6 * 6) = 720 / 36 = 20

So, Laura has 20 different combinations of 3 scoops of ice cream to choose from.

This is not a scenario where repetition is allowed, because once a flavor has been chosen, it can't be chosen again for the same serving of ice cream.

Answer 2

can't be more than 18 right because 6 times 3