Chapter 9.1, Problem 38E

Solution

To state: The number of different ways in which a customer can order a car if he has to choose from 3 models, each of which comes in 4 exterior colors, in 3 interior colors, and with combination of up to 6 optional accessories.

The resultant value is 2304 ways.

Given information:

A customer has to choose from 3 models, each of which comes in 4 exterior colors, in 3 interior colors, and with combination of up to 6 optional accessories.

Explanation:

Number of models available are 3. Then the number of ways in which a model can be selected is: 3

Number of exterior colors are 4. Then the number of ways in which an exterior color can be selected is: 4

Number of interior colors are 3. Then the number of ways in which an interior color can be selected is: 3

Number of optional accessories are 6. Selecting each accessory has two possible options selecting it or not selecting it.

Then the number of ways in which an accessory can be selected is: $2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2=64$

The total number of ways in which a customer can select a car is:

  $3\cdot 4\cdot 3\cdot 64=2304$

Therefore, there are 2304 ways in which a customer can select a car.