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15 February, 09:16

I have 6 shirts, 6 pairs of pants, and 6 hats. Each item comes in the same 6 colors (so that I have one of each item of each color). I refuse to wear an outfit in which all 3 items are the same color. How many choices for outfits do I have?

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  1. 15 February, 12:03
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    210 is the number of clothing choices.

    Step-by-step explanation:

    From exercise we have 6 shirts, 6 pairs of pants, and 6 hats.

    We calculate the number of all possible combinations, and we get

    6 · 6 · 6 = 216

    The number of combinations when all 3 items are the same color is 6.

    Therefore, the number of appropriate combinations is as follows

    216-6=210.

    210 is the number of clothing choices.
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