SOLUTION: I need help figuring out the formula for this word problem: "Suppose a university faculty is establishing a search committee to hire a new president and there are 150 Men and 50

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Question 782035: I need help figuring out the formula for this word problem:
"Suppose a university faculty is establishing a search committee to hire a new president and there are 150 Men and 50 Women and the Board of Trustees has suggested that they want exactly 2 women on the 5 person committee. Suppose the faculty insist on putting the names of all faculty in a hat and drawing out 5 at random. What is the probability that choosing the committee at random will result in a committee that is acceptable to the Board of Trustees."
Answer by stanbon(75887) (Show Source):
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"Suppose a university faculty is establishing a search committee to hire a new president and there are 150 Men and 50 Women and the Board of Trustees has suggested that they want exactly 2 women on the 5 person committee. Suppose the faculty insist on putting the names of all faculty in a hat and drawing out 5 at random. What is the probability that choosing the committee at random will result in a committee that is acceptable to the Board of Trustees."
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# of ways to succeed:: 50C2*150C3 = 675342500
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# of random groups of 5:: 200C5 = 2535750040
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Divide to get the probability:: 0.2663
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Cheers,
Stan H.
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