From a group of 4 men and 5 women a committee of 4 is to be selected. a) How man

Question

From a group of 4 men and 5 women a committee of 4 is to be selected. a) How many committees are there if two of the women refuse to serve together ? b) What is the probability of having at least 1 woman ? c) What is the probability of the committee being evenly split between men and women ? From a group of 4 men and 5 women a committee of 4 is to be selected. a) How many committees are there if two of the women refuse to serve together ? b) What is the probability of having at least 1 woman ? c) What is the probability of the committee being evenly split between men and women ? From a group of 4 men and 5 women a committee of 4 is to be selected. a) How many committees are there if two of the women refuse to serve together ? b) What is the probability of having at least 1 woman ? c) What is the probability of the committee being evenly split between men and women ?

Explanation / Answer

a) No of committees = 9C4 - 7C2 = 105

b) P(at least one woman) = (5C1 * 4C3 + 5C2 * 4C2 + 5C3 * 4C1 + 5C4)/9C4 = 0.992

c) Probability = (5C2 * 4C2)/9C4 = 0.476

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