5. A national committee is to be comprised of a represenative from each of the f

Question

5. A national committee is to be comprised of a represenative from each of the fifty states, the District of Columbia, Puerto Rico, and Guam. For the states, the representative is either the governor or one of the two state senators. For DC, the representative is the mayor; for Puerto Rico, the representative is either the governor, the President of the Senate, the Speaker of the House, or the Chief Justice of the Supreme Court of Puerto Rico; and for Guam, it is the governor. How many committees are possible? 6. How many ways can a supervisor with 25 employees select ten employees to be in a focus group if: (a) Xavier and Yoda must be in the focus group; (b) either Xavier or Yoda, but not both, must be in the focus group; (c) neither Xavier nor Yoda are in the focus group.

Explanation / Answer

No. of ways of selecting a representative from 50 states = 3

No. of ways=3^50

DC - 1 way

Guam-1

Peurto Rico = 4 ways

Total no. of committees = 3^50 * 4

b)

Both in focus group = 23C8 = 23!/(8! * 15!)

Either in focus group = 2 * 23C9 = 2* 23!/[9!*14!]

Neither in group = 23C10 = 23!/[13!*10!]

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