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?

Answer 1

Answer:

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.