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 complementary 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 options for the principal color, 5 remaining options for the complementary color, 4 options for the accent color, and 3 options for the last color. Thus, the number of possible combinations for one unit is:
6 x 5 x 4 x 3 = 360
Since repetitions are permitted, each of these 360 combinations can be used for any of the 4 color slots. Thus, the total number of different units that can be decorated is:
360^4 = 1,296. Therefore, option D is the correct answer.

Six Basic Colors Are Used in Decorating a New Condominium