A juggling club has 5 male members and 4 female members.
a) I know the answer to this: "How many nonempty sets of juggling club members can be chosen to perform in a show" is Answer: 2^9 - 1. However,
b) How many nonempty subsets of juggling club members containing at least one female can be chosen? Answer: Shouldn't it be 2^9 - 2^5 - 1? My professor had the answer as just 2^9 - 2^5 without the minus one. But we still need to exclude the empty set right?
Also how can we solve this using n choose k? I am really starting to understand n choose k and it's relation with Pascal's Triangle, but I would like to apply it to this question here.