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14 December, 00:13

An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women. If the committee members are chosen randomly, what is the probability that precisely half of the members will be women?

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  1. 14 December, 00:39
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    5/33649 = approx 0.00015

    Step-by-step explanation:

    Total number of outcomes are C24 6 = 24! / (24-6) !/6!=19*20*21*22*23*24 / (2*3*4*5*6) = 19*14*22*23

    Half of the Committee = 3 persons. That mens that number of the women in Commettee=3. 3 women from 6 can be elected C6 3 ways (outputs) =

    6!/3!/3!=4*5*6*/2/3=20

    So the probability that 3 members of the commettee are women is

    P (women=3) = 20 / (19*14*22*23) = 5 / (77*19*23) = 5/33649=approx 0.00015
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