SOLUTION: A committee of three is selected at random from a set consisting of five Democrats, eight Republicans,and two Independents. (a) What is the probability that the committee consists

Question 209866: A committee of three is selected at random from a set consisting of five Democrats, eight Republicans,and two Independents.
(a) What is the probability that the committee consists of all Democrats?
(b) What is the probability that the committee consists of no Republicans?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A committee of three is selected at random from a set consisting of five Democrats, eight Republicans,and two Independents.
(a) What is the probability that the committee consists of all Democrats?
# of ways to select 3 Democrats: 5C3 = 10
# of ways to pick 3 from the group: 15C3 = 455
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P(pick 3 Demoncrats) = 10/455
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(b) What is the probability that the committee consists of no Republicans?
# of ways to pick no Republicans: 7C3
# of ways to pick 3 from the group: 15C3
P(pick 3 that are not Republicans) = 7C3/15C3 = 35/455
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Cheers,
Stan H.
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