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(Solved): Twenty People Work At A Small Startup. A Six-person Committee Is To Be Formed. (a) Let D Denote The ...

  1. Twenty people work at a small startup. A six-person committee is to be formed.

    1. (a) Let D denote the set of all possible committees. Find |D|.

    2. (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|.

    3. (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|.

    4. (d) Find |P ? Q|.

    5. (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.

    6. (f) Find |S|.

    7. (g) How many committees can we form with no unhappy employees?

    8. (h) Instead of one committee, we decide to form two six-person commit- tees. Each employee can be on at most one committee. How many ways can we form these committees, if employee happiness is nottaken into consideration?

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