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

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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) About Me  (Show Source):
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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.