Question

Two roommates live in a dorm. Their mother's both shop at the same stores and have the same taste, so they both have the same 3 pairs of shoes, the same 3 pairs of pants, the same 3 shirts, and the same three sweaters. How many ways can they dress so that are not both dressed exactly the same.

Answer 1

For each of the 3×3×3×3 = 81 ways the first mom can dress, the second can dress 80 ways and not be exactly the same. The number of permutations of dress will be ...

... 81×80 = 6480