Use the Fundamental Counting Principle to solve Exercises 29–40. An ice cream store sells two drinks (sodas or milk shakes) in four sizes (small, medium, large, or jumbo) and five flavors (vanilla, strawberry, chocolate, coffee, or pistachio). In how many ways can a customer order a drink?

Verified step by step guidance

1. Identify the categories involved in the problem. Here, the categories are: type of drink, size of the drink, and flavor of the drink.
2. Determine the number of options in each category. There are 2 types of drinks (sodas or milk shakes), 4 sizes (small, medium, large, jumbo), and 5 flavors (vanilla, strawberry, chocolate, coffee, pistachio).
3. Apply the Fundamental Counting Principle, which states that if there are multiple categories of choices, the total number of combinations is the product of the number of options in each category.
4. Write the multiplication expression to find the total number of ways to order a drink: \$2 \times 4 \times 5$.
5. Multiply the numbers to find the total number of possible drink orders (do not calculate the final product here, just set up the expression).

Key Concepts

Fundamental Counting Principle

The Fundamental Counting Principle states that if there are multiple independent choices to be made, the total number of outcomes is the product of the number of options for each choice. For example, if there are 2 drink types and 4 sizes, the total combinations for these two choices is 2 × 4.

Independent Choices in Combinatorics

Independent choices mean that the selection of one option does not affect the selection of another. In this problem, choosing a drink type, size, and flavor are independent decisions, so their possibilities multiply to find the total number of unique orders.

Multiplication of Multiple Categories

When dealing with several categories (like drink type, size, and flavor), multiply the number of options in each category to find the total number of combinations. Here, multiply 2 (drinks) × 4 (sizes) × 5 (flavors) to get the total possible drink orders.