A committee of three is to be chosen from a group of four women and three men. What is the probability that the committee will consist of one man and two women?

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BlackTom AI · Accepted Answer

Let me restate the problem in my own words to ensure understanding: we have a pool of 4 women and 3 men, and we want the probability that a randomly formed committee of 3 people contains exactly 1 man and 2 women.

First, determine the total number of possible 3-person committees from the 7 people. This is a combination problem: C(7,3) = 35 total committees.

Next, count the favorable committees that have exactly 1 man and 2 women. To form such a committee, we must choose:
- 1 man from the 3 available men: C(3,1) = 3 ways
- 2 women from the 4 available women: C(4,2) = 6 ways

Multiply these because the choices are independent: 3 × 6 = 18 favorable committees.

Therefore, the probability is the number of favorable outcomes over the total outcomes: 18/35.

If you compare to the provided answer label (such as d. 18/35), this matches the computed probability. Note: since the actual list of answer options was not included in the data here, I’m focusing on the calculation that yields the 18/35 result and how it aligns with the given solution format.

MUF0092 Mathematics Unit 2-SEM 1-2025 9.8 Entire Study Area 2 Revision Questions

A committee of three is to be chosen from a group of four women and three men. What is the probability that the committee will consist of one man and two women?

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