Use the Fundamental Counting Principle to solve Exercises 29–40. The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or sport). In how many ways can you order the car?

Verified step by step guidance

1. Identify the number of choices for each category. Here, there are 9 different colors and 3 different styles (hatchback, sedan, sport).
2. Recall the Fundamental Counting Principle, which states that if one event can occur in m ways and a second event can occur in n ways, then the two events together can occur in m × n ways.
3. Apply the principle by multiplying the number of color options by the number of style options: $9\times 3$.
4. Set up the multiplication expression to find the total number of ways to order the car: $9\times 3=\; ?$.
5. Calculate the product to find the total number of possible car orders (do this calculation yourself to complete the solution).

Key Concepts

Fundamental Counting Principle

The Fundamental Counting Principle states that if one event can occur in m ways and a second independent event can occur in n ways, then the two events together can occur in m × n ways. This principle helps calculate the total number of possible outcomes when multiple choices or events are combined.

Independent Choices

Independent choices mean that the selection of one option does not affect the selection of another. In this problem, choosing a car color does not influence the choice of style, so the total number of combinations is the product of the number of color options and style options.

Multiplication of Options

When multiple categories of options are available, the total number of unique combinations is found by multiplying the number of choices in each category. Here, multiplying 9 colors by 3 styles gives the total ways to order the car.