At a local vehicle dealership, a buyer customizing a new car model can select 1 exterior p… — ACT

At a local vehicle dealership, a buyer customizing a new car model can select $1$ exterior paint color from $5$ available colors, $1$ interior seat material from $3$ available materials, and $1$ transmission type from $2$ available options (manual or automatic). According to the Fundamental Counting Principle, how many different unique configurations of the car can a buyer create?

Answer: 30 configurations

Answer

There are 30 different unique configurations possible.

According to the Fundamental Counting Principle, when making a series of independent choices, the total number of distinct outcomes is found by multiplying the number of options for each choice. Multiplying 5 exterior colors, 3 interior materials, and 2 transmission types gives

5 \times 3 \times 2 = 30

unique car configurations.

Step-by-Step Solution

Count the number of choices for each feature

Paint colors = 5, Interior materials = 3, Transmissions = 2

Each feature selection is an independent choice in the configuration process.

Multiply the number of options for all features

5 \times 3 \times 2 = 30

The Fundamental Counting Principle states that if there are

n_1

ways to make one choice,

n_2

ways to make a second, and

n_3

ways to make a third, the total number of combined outcomes is

n_1 \times n_2 \times n_3

Key Concept

Fundamental Counting Principle

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