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# A committee of three people is to be randomly selected

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A committee of three people is to be randomly selected from a group of three men and two women, and the chairperson will be randomly selected from the committee. What is the probability that the committee will have exactly two women and one man, and that the chairperson will be a man? Express your answer as a common fraction.

Nov 3, 2020

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Out of the five people, there is a $$\frac{2}{5} \cdot \frac{1}{4} = \frac{2}{20} = \frac{1}{10}$$ chance that the commitee will have exactly two women and one man. And there is a $$\frac{1}{10} \cdot \frac{1}{3} = \frac{1}{30}$$ chance that the chairperson will be a man.

I'm not 100% sure this answer is correct, someone should double check it :D

Nov 3, 2020
edited by SqltyPi  Nov 3, 2020