Question

A car manufacturer advertises that it offers 72 unique cars that can be created from the exterior, interior, and seat styles it offers. Determine how many different seat styles the manufacturer can off if there are 12 different exterior colours and 2 different interior colours.

Answer 1

The manufacturer can offer 3 different seat styles, calculated by dividing the total number of unique car variations (72) by the product of the number of exterior colors (12) and interior colors (2).

Step-by-step explanation:

To determine the number of different seat styles the car manufacturer can offer, given that 72 unique cars can be created from the available options, we use the fundamental counting principle. The principle states that if there are p ways to do one thing and q ways to do another, then there are p * q ways to do both.

In this case, the car manufacturer offers 12 different exterior colors and 2 different interior colors. Let's call the number of different seat styles s. Since the total number of unique cars is 72, we can set up the equation:

12 (exterior colors) * 2 (interior colors) * s (seat styles) = 72

Solving for s, we get:

24s = 72

s = 72 / 24

s = 3

Therefore, the manufacturer can offer 3 different seat styles.