Each day for a week I have the choice of wearing a hat and/or sunglasses. How many ways can I do this so that on one or more days I do neither?

Question

Please help. I am assuming that this question uses combinations and permutation but I'm not sure even where to begin. Please help.

Answer 1

I believe this just a Fundamental Counting Principle question. Six days you have four choices (Hat, Sunglasses, Both, Neither). On the seventh you only have one choice, neither, since you have to do neither at least one day. So the number of ways this can be done are 4^6=4096 ways.