192 ways that Fred can dress for the week
Outfit Choices: 7 Days
Angel
Fred is looking to pick out his clothes for the next 7 days. He has two different pairs of pants and
two different shirts. Each day he needs to wear a different outfit than what he wore the day before.
However, he has already chosen his outfit for Friday due to a formal occasion. How many ways can he
dress for the week?
Since Fred has already chosen his outfit for Friday, he only needs to choose 6 outfits for the remaining days of the week (Saturday through Thursday).
For each day, he has 2 choices for pants and 2 choices for shirts. So there are 2 × 2 = 4 possible outfits for each day.
To make sure he wears a different outfit each day, Fred needs to choose a different outfit from the previous day's outfit. For Saturday, he has 4 choices. For Sunday, he has 3 choices (since he cannot wear Saturday's outfit), and so on, until Thursday, for which he has only 1 choice.