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?

Question

Mathematics

Patrick Mcneil

3 April, 16:29

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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Answers (1)

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Ayaan Barnett · Answer 1

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