Problem 66 - College Algebra

Question

Solve by the method of your choice. 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

There are 4495 possible bowls.

Step 1: Understanding Combinations

A combination is a selection of items from a larger set, where the order of selection does not matter. In this case, we are choosing 3 flavors out of 31, and we do not care about the order in which they are selected. We can represent this mathematically as \( C(n, r) \), where n is the total number of items and r is the number of items to be selected.

Step 2: Using the Combinations Formula

This formula is \( C(n, r) = \frac{n!}{r!(n-r)!} \). The symbol \( ! \) denotes a factorial, meaning you multiply the number by every positive integer less than itself. Using this formula, we substitute \( n = 31 \) and \( r = 3 \) .

Step 3: Calculating our Answer

Substituting our values into the formula, we have \( C(31,3) = \frac{31!}{3!(31-3)!} \). We then simplify this expression to get our answer.