### Instruction: 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?### Response: I could start by counting the total number of possible outfits, without any restrictions.
That would be 6 x 6 x 6 = 216, since I have 6 choices for each item.
But some of those outfits would violate my rule of not wearing all 3 items of the same color.
How many of those are there?
Well, for each of the 6 colors, there is exactly one outfit that is all that color: the shirt, pants, and hat of that color.
So there are 6 outfits that I need to exclude from the total.
Therefore, the number of choices for outfits that I have, following my rule, is 216 - 6 = 210.