Problem 66 - Algebra and Trigonometry

Question

Baskin-Robbins offers 31 different flavors of ice cream. One of its items is a bowl consisting of three scoops of ice cream, each a different flavor. How many such bowls are possible?

Step-by-Step Solution

Answer

The number of ways to choose 3 flavors out of 31 is given by \( C(31, 3) = 4495 \). So, there are 4495 possible flavor combinations.

Step 1: Identify n and r in the combination formula

We are given that Baskin-Robbins offers 31 flavors of ice cream and we want to choose 3 out of them. For our combination formula, n is the number of total items, and r is the number of items to choose, so in our case n is 31 (total flavors) and r is 3 (number of scoops).

Step 2: Apply the combination formula

Now, apply the combination formula, which is \( C(n, r) = \frac{n!}{r!(n-r)!} \). Replace n and r with 31 and 3 respectively. So our formula becomes \( C(31, 3) = \frac{31!}{3!(31-3)!} \).

Step 3: Simplify the equation

Calculate the value of \(31!\), \(3!\), and \((31-3)!\), and simplify the equation to get the number of possible flavor combinations for the bowl.