jmc

Question

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?

Accepted Answer

The number of all outfit combinations is 6 6 6=216. There are 6 outfits in which all three items are the same color. Thus there are 216-6=210 outfits in which not all three items are the same color.