From a group of 7 men and 4 women a committee of 6 persons is formed. What is the probability that the committee will consist of exactly 2 women?
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Answer:
5/11
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From a group of 7 men and 4 women a committee of 6 persons is formed. What is the probability that the committee will consist of exactly 2 women?
Men = 7
Women = 4
Commitee of 6 can be :
2M 4W , 3M3W , 4M2W , 5M1W , 6M
⁷C₂⁴C₄ + ⁷C₃⁴C₃ + ⁷C₄⁴C₂ + ⁷C₅⁴C₁ + ⁷C₆
= 21 * 1 + 35*4 + 35*6 + 21*4 + 7
= 21 + 140 + 210 + 84 + 7
= 462
probability that the committee will consist of exactly 2 women = ⁷C₄⁴C₂/462
= 210/462
= 5/11
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