Six basic colours are to be used in decorating a new condominium. They are to be applied to a unit in groups of four colours. One unit might have gold as the principal colour, blue as a complementary colour, red as the accent colour and touches of white. Another unit might have blue as the principal colour, white as the complimentary colour, gold as the accent colour and touches of red. If repetitions are permitted, how many different units can be decorated?
A) 7,825
B) 24
C) 125
D) 1,296

Question

Quizplus · Accepted Answer

There are 6 choices for the principal colour, and for each of those choices, there are 5 choices for the complementary colour (since it cannot be the same as the principal colour). For each of those 6*5 = 30 combinations, there are 4 choices for the accent colour. Finally, there are 6 choices for the touches of a fourth colour. Therefore, the total number of units that can be decorated is 6 x 5 x 4 x 6 = 1,296.

Six Basic Colours Are to Be Used in Decorating a New