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A committee of 5 persons is to be randomly selected from a group of 5 men and 4 women and a chairperson will be randomly selected from the committee. The probability that the committee will have exactly 2 women and 3 men and the chairperson will be a man is p, then 1 p is equal to

Correct answer

3.5

Step-by-step solution

Total cases = C 9 5 × C 5 1 ( ∴ there are 5 ways to choose a chairperson) Favourable cases = 3 men can be chosen in C 5 3 ways, 2 women can be chosen in C 4 2 ways and there are 3 ways to choose the chairperson Total number of favourable ways = C 5 3 × C 4 2 × 3 Required probability = C 5 3 × C 4 2 × 3 C 9 5 × 5 = 10 × 6 × 3 126 × 5 = 2 7

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