Question

The local ice cream shop in Dontrelle's town is called 21 Choices. Why? Because they offer 21 different flavors of ice cream. Dontrelle's sister Emogene wants to order a small cup with 2 scoops of different flavors. In how many ways can she do this? (Note that the order of the 2 flavors doesn't matter.)

Answer 1

Emogene can choose 2 different flavors in 210 different ways from the selection of 21 flavors at the ice cream shop, since the order of flavors doesn't matter.

Step-by-step explanation:

The question: Emogene wants to order a small cup with 2 scoops of different flavors from a selection of 21 different flavors. In how many ways can she do this, assuming the order of the flavors doesn't matter?

To find the number of combinations, we can use the formula for combinations without repetition which is C(n, k) = n! / (k! (n - k)!), where n is the total number of items to choose from, and k is the number we want to choose. In this case, n = 21 (the number of ice cream flavors) and k = 2 (the number of scoops).

So, the calculation becomes:

C(21, 2) = 21! / (2! (21 - 2)!) = 21! / (2! 19!) = (21 × 20) / (2 × 1) = 210

Therefore, Emogene can choose 2 different flavors in 210 different ways.