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Rework problem 24 from section 3.2 of your text, involving the subcommittee. For this problem, assume...

Rework problem 24 from section 3.2 of your text, involving the subcommittee. For this problem, assume that the committee contains 6 men and 8 women and that three are selected at random for a subcommittee. What is the probability that the subcommittee consists of 2 men and 1 woman, given that it contains both men and women?

Math   Statistics-And-Probability   
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Answer #1

Given that,

Committee has 6 men and 8 women.

Total members= 14

3 are selected for a sub-committee which contains both men and women.

Number of ways of selecting 3 from 14 members= 14C3

We need to find the probability that the subcommittee consists of 2 men and 1 woman.

Number of ways of selecting 2 men from 6 men= 6C2

Number of ways of selecting 1 woman from 8 men= 8C1

The probability that the subcommittee consists of 2 men and 1 woman, given that it contains both men and women   

So, required probability= 30/91

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