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12 October, 19:24

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?

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  1. 12 October, 20:41
    0
    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
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