I have 6 shirts, 4 pairs of pants, and 6 hats. The pants come in tan, black, blue, and gray. The shirts and hats come in those colors, and also white and yellow. I refuse to wear an outfit in which all 3 items are the same color.

How many choices for outfits, consisting of one shirt, one hat, and one pair of pants, do I have?

80

Step-by-step explanation:

If one event can occur in m ways and a second event can occur in n ways after the first event has occurred and a third event can occur in o ways after the first and second numbers have occurred then the three events can occur in m x n x o ways. This is also known as the Fundamental Counting Principle.

4 pants

6 shirts

6 hats

If the combination can be any color

Then the total number hats pant and shirt combination should be

Shirt x hat x pant

6 x 6 x 4 = 144

But because I don't want to wear same color combination of hat, shirt and pant then the subsequent occurrence will have 1 less option to choose from

Combination will therefore be

Pant x hat less 1 color x shirt less 2 color

4 x 5 x 4 = 80 combinations