Question 841894: 9. (12 pts) An advisory panel of 5 students is to be chosen from a group of 12 student volunteers.
(a) In how many ways can the advisory panel be chosen? Show work/explanation.
(b) Now suppose that the group of student volunteers consists of 6 seniors, 4 juniors, and 2 sophomores. In how many ways can the 5-person advisory panel be chosen if it must consist of 2 seniors, 2 juniors, and 1 sophomore? Show some work/explanation.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An advisory panel of 5 students is to be chosen from a group of 12 student volunteers.
(a) In how many ways can the advisory panel be chosen? Show work/explanation.
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Use "combinations" to count groups of people.
Ans: 12C5 = (12*11*10*9*8)/(1*2*3*4*5) = 792
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(b) Now suppose that the group of student volunteers consists of 6 seniors, 4 juniors, and 2 sophomores. In how many ways can the 5-person advisory panel be chosen if it must consist of 2 seniors, 2 juniors, and 1 sophomore? Show some work/explanation.
Ans: 6C2*4C2*2C1 = 15*6*2 = 180 ways
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Cheers,
Stan H.
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