There are 6 men and 7 women in a committee. 2 people need to be selected as…
2024
There are 6 men and 7 women in a committee. 2 people need to be selected as representative of this committee. What is the probability , that out of these 2 people, 1 is a man and another is a woman ?
- A.
3/13
- B.
7/26
- C.
5/26
- D.
7/13
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Correct answer: D
Answer: 7/13
Key steps:
Total ways to choose any 2 people from 13 = C(13,2) = 78.
Number of ways to choose 1 man from 6 and 1 woman from 7 = 6 * 7 = 42.
Therefore probability = favourable / total = 42 / 78 = 7/13.
Alternate combination form: (6 choose 1)*(7 choose 1) / (13 choose 2) = 7/13.