5. 1.2-11. Three students (S) and six faculty members (F) are on a panel discuss

Question

5. 1.2-11. Three students (S) and six faculty members (F) are on a panel discussing a new college policy (a) In how many different ways can the nine participants be lined up at a table in the front of the auditorium? (b) How many lineups are possible, considering only the labels S and F? (c) For each of the nine participants, you are to decide whether the participant did a good job or a poor job stating his or her opinion of the new policy; that is, give each of the nine participants a grade of G or P. How many different scorecards are possible?

Explanation / Answer

a) number of ways 3 S and 6 F can be arranged =
= (3+6)! = 9!

b)
considering only labels S and F
number of ways = 9!/(3! *6!) = 9 * 8 *7 / 6 = 84

c)
each of member can give 2 different opinion
hence
number of different scorecard = 2^9

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