Three students (S) and six faculty members (F) are on a panel discussing a new c
ID: 3438474 • Letter: T
Question
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.
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]
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