Final answer:
The probability of choosing a committee of three with exactly two men from a group of 4 men and 5 women at random is 5/14. This involves finding the combinations of men and women separately, then dividing the favorable outcomes by the total possible committees formed. Thus, the correct answer is (a) 5/14.
Step-by-step explanation:
The question asks us about the probability of choosing exactly two men from a group of 4 men and 5 women to form a committee of three. This is a problem that involves combinations and probability.
Firstly, we calculate the number of ways to choose 2 men from 4, which is C(4,2). Secondly, we calculate the number of ways to choose 1 woman from 5, which is C(5,1). To find the total number of favorable outcomes, we multiply these two results.
Total favorable outcomes = C(4,2) * C(5,1)
Now, we calculate the total number of ways to form a committee of three from all 9 people, which is C(9,3).
The probability is then:
P(Exactly 2 men) = Total favorable outcomes / Total possible committees
The exact calculations give: (6 * 5) / 84 = 30 / 84, which simplifies to 5/14. Thus, the correct answer is (a) 5/14.