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Chapter 11: Problem 13

A person can order a new car with a choice of six possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options?

Short Answer

Expert verified
There are 96 different ways to order a new car with regard to these options.

Step by step solution

01

Set Up the Problem

The problem involves multiple independent decisions that a buyer can make when ordering a new car. There are 6 options for the color, 2 options for air-conditioning - with or without, 2 options for transmission - automatic or manual, 2 options for power windows - with or without, and 2 options for a CD Player - with or without.
02

Apply the Multiplication Principle

According to the multiplication principle, if there are m ways to do one thing, and n ways to do another, then there are m*n ways to perform both actions. Therefore, the total number of ways these decisions can be combined is the product of their individual decision counts: 6 (color) * 2 (air-conditioning) * 2 (transmission) * 2 (windows) * 2 (CD).
03

Calculate the Total Number of Ways

Multiplying the individual decision counts together, 6 * 2 * 2 * 2 * 2, it results in a total of 96 unique ways to order a car.

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