SOLUTION: 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 complemen

Question 1096509: 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?
How do I explain how I got my answer of 1,296? I know its rules of multiplication, but I don't know how to explain my answer to my professor.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
There are 6 colors to choose from for the first
Each of those has 6 possibilities for the second in the group, since repetition is allowed. That is 6*6=36
Each of those has 6 possibilities for the third, which is 6*6*6=216
and each of those has 6 possibilities for the fourth.
This is 6^4 or 1296.
A tree diagram for one color would show the fourth power and that would be multiplied by 4.
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