EXAMPLE 3.3.9

Gomer's Auto Body Shoppe is still trying to unload some surplus paint by offering the following special deals:

For $99 you get a two-tone paint job, using one color for the car's top and a different color for the body.

For $129 you get a three-tone paint job, using one color for the car's top, a different color for the body, and a third color for the hub caps.

The available colors are:

1. hot pink

2. puke green

3. Gator orange

4. flaming chartreuse

How many different color schemes are possible?

A. 24

B. 36

C. 27

D. none of these

SOLUTION

A paint job will be either two-tone or three-tone, so the number of possible paint schemes will be the number of possible two-tone paint schemes plus the number of possible three-tone paint schemes.

Number of two-tone paint schemes

Choosing a two-tone paint scheme requires that we make two dependent decisions:

1. Choose color for top: 4 options

2. Choose color for body: 3 options

The number of two-tone paint schemes is

(4) times (3) = 12

Number of three-tone paint schemes

Choosing a three-tone paint scheme requires that we make three dependent decisions:

1. Choose color for top: 4 options

2. Choose color for body: 3 options

3. Choose color for hub caps: 2 options

The number of three-tone paint schemes is

(4) times (3) times (2) = 24

Thus, the total number of paint possible paint schemes is 12 + 24 = 36.