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There are 5 men and 3 women. A committee of 3 members is to be made. Find the probability that either there are 2 men and 1 woman or 2 women and 1 man.
  • a)
    5/51
  • b)
    45/56
  • c)
    35/51
  • d)
    48/61
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
There are 5 men and 3 women. A committee of 3 members is to be made. F...
2 men and 1 woman, prob. = 5C2 * 3C1 / 8C3 
2 women and 1 man, prob. = 5C1 * 3C2 / 8C3
Add both cases
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Most Upvoted Answer
There are 5 men and 3 women. A committee of 3 members is to be made. F...
Calculation:
- Total number of ways to choose a committee of 3 members out of 8 people = 8C3 = 56
- Number of ways to choose 2 men and 1 woman = 5C2 * 3C1 = 10 * 3 = 30
- Number of ways to choose 2 women and 1 man = 3C2 * 5C1 = 3 * 5 = 15
- Total number of favorable outcomes = 30 + 15 = 45

Probability Calculation:
- Probability = Number of favorable outcomes / Total number of outcomes
- Probability = 45 / 56 = 45/56
Therefore, the probability that either there are 2 men and 1 woman or 2 women and 1 man is 45/56.
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There are 5 men and 3 women. A committee of 3 members is to be made. Find the probability that either there are 2 men and 1 woman or 2 women and 1 man.a)5/51b)45/56c)35/51d)48/61e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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