Adele is buying a sport utility vehicle. She is trying to choose among a variety of options.

Question

Brand: Brand A or Brand B

Transmission: 4-speed standard, 5-speed standard, or automatic

Bumper: steel, vinyl, or 2x4 boards

Roof: hard top or convertible top

Adele calculates that she has 2 + 3 + 3 + 2, or a total of 10, possible vehicle choices

What is Adele’s error?
She should have added only the transmission and bumper choices.
She should have added only the brand and roof choices.
She should have multiplied the total of all the choices.
She should have multiplied only the brand and roof choices.

Answer 1

Adele's error is that she should have multiplied the total of all the choices rather than adding them. In this case, each option is independent of the others, which means the total number of combinations is found by multiplying the number of choices for each category together.

To calculate the total combinations correctly:

• Brands: 2 options (Brand A or Brand B)
• Transmissions: 3 options (4-speed standard, 5-speed standard, automatic)
• Bumpers: 3 options (steel, vinyl, or 2x4 boards)
• Roofs: 2 options (hard top or convertible top)

So, the total number of vehicle combinations would be:

\[ 2 \times 3 \times 3 \times 2 = 36 \]

Therefore, the correct answer is: She should have multiplied the total of all the choices.