Twenty people work at a small startup. A six-person committee is to be formed. (a) Let D denote the set of all possible committees. Find |D|. (b) Two of the workers, Alice and Beth, will be unhappy if they have to serve together. Let P be the set of possible committees with both Alice and Beth. Find |P|. (c) Beth will also be unhappy if she has to serve with both Frank and Grace. Let Q be the set of possible committees on which Beth, Frank, and Grace would all serve together. Find |Q|. (d) Find |P ∩Q|. (e) Let S be the set of all possible committees on which there is at least one unhappy employee. Express S in terms of only P and Q. (f) Find |S|. (g) How many committees can we form with no unhappy employees? (h) Instead of one committee, we decide to form two six-person committees. Each employee can be on at most one committee. How many ways can we form these committees, if employee happiness is not taken into consideration?