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: drink type, size, and flavor.
2. Determine the number of options in each category: 2 drink types, 4 sizes, and 5 flavors.
3. Recall the Fundamental Counting Principle, which states that if there are $n$ ways to do one thing and $m$ ways to do another, then there are $n\backslash timesm$ ways to do both.
4. Apply the principle by multiplying the number of options in each category: $2\; \backslash times\; 4\; \backslash times\; 5$.
5. The product gives the total number of ways a customer can order a drink considering all combinations of drink type, size, and flavor.

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 = 8.

Multiplication of Independent Events

When choices or events do not affect each other, their total number of combinations is found by multiplying the number of options for each event. In this problem, choosing a drink type, size, and flavor are independent events, so multiply the number of options for each to find total possibilities.

Counting Combinations in Real-World Contexts

Applying counting principles to practical problems involves identifying all categories and their options, then combining them correctly. Here, the categories are drink type, size, and flavor, and understanding how to count all possible orders helps solve the problem efficiently.