Need Help ?
Have a Question ?

(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?

Expert Answer


We have an Answer from Expert Buy This Answer $6