Three students S and six faculty members F are on a panel di

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?

Solution

a.

Persons are all distinct.

Thus, there are 9! = 362880 ways to arrange them on a line. [answer]

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b.

Using the formula for permuations of like objects on a line,

N = (3 + 6)! / (3! 6!) = 84 [ANSWER]

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c.

There are 9 participants, and 2 possible scorecards for each.

Thus, there are 2*2*2*2*2*2*2*2*@ = 2^9 = 512 different scorecards. [ANSWER]