Six basic colors are used in decorating a new condominium. They are applied to a unit in groups of four colors. One unit might have gold as the principal color, blue as a complementary color, red as the accent color and touches of white. Another unit might have blue as the principal color, white as the complimentary color, gold as the accent color and touches of red. If repetitions are permitted, how many different units can be decorated?
A) 7,825
B) 25
C) 125
D) 1,296

Question

Quizplus · Accepted Answer

There are 6 choices for the principal color, 5 choices for the complementary color (since it cannot be the same as the principal color), 4 choices for the accent color, and 2 choices for the fourth touch color (either white or red, depending on the previous choices). Therefore, the total number of possible units is:

6 × 5 × 4 × 2 = 240 for each distinct combination of principal, complementary, and accent colors.

Since there are 6 distinct combinations of these three colors (e.g. gold-blue-red, blue-white-gold, etc.), the total number of possible units is:

240 × 6 = 1,440.

However, repetitions are allowed, so we need to account for the fact that each unit can be decorated in 4 different ways (since the order of the colors doesn't matter). Thus, the final answer is:

1,440 ÷ 4 = 360.

Therefore, the best choice is (D) 1,296.

Six Basic Colors Are Used in Decorating a New Condominium