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A committee of 4 people is to be formed from 3 men, 2 women and 4 children. What is the probability that exactly two of chosen people are children?
- a)13/21
- b)10/31
- c)5/21
- d)10/21
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A committee of 4 people is to be formed from 3 men, 2 women and 4 chil...
2 children should be there and rest 2 either from (2 women + 3 men) 5 people
So prob. = 4C2 * 5C2 / 9C4
So prob. = 4C2 * 5C2 / 9C4
Most Upvoted Answer
A committee of 4 people is to be formed from 3 men, 2 women and 4 chil...
Approach:
To find the probability of exactly two children being chosen for the committee, we need to calculate the total number of ways to select 4 people from the total pool of 3 men, 2 women, and 4 children, as well as the number of ways to choose 2 children and 2 other people (men or women).
Calculations:
- Total ways to choose 4 people out of 9: 9C4 = 126
- Ways to choose 2 children out of 4: 4C2 = 6
- Ways to choose 2 other people out of 5 (men and women): 5C2 = 10
- Total number of ways to choose 2 children and 2 other people: 6 * 10 = 60
Probability:
Probability = Number of favorable outcomes / Total outcomes
Probability = 60 / 126 = 10 / 21
Therefore, the probability that exactly two of the chosen people are children is 10/21, which corresponds to option 'D'.
To find the probability of exactly two children being chosen for the committee, we need to calculate the total number of ways to select 4 people from the total pool of 3 men, 2 women, and 4 children, as well as the number of ways to choose 2 children and 2 other people (men or women).
Calculations:
- Total ways to choose 4 people out of 9: 9C4 = 126
- Ways to choose 2 children out of 4: 4C2 = 6
- Ways to choose 2 other people out of 5 (men and women): 5C2 = 10
- Total number of ways to choose 2 children and 2 other people: 6 * 10 = 60
Probability:
Probability = Number of favorable outcomes / Total outcomes
Probability = 60 / 126 = 10 / 21
Therefore, the probability that exactly two of the chosen people are children is 10/21, which corresponds to option 'D'.
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A committee of 4 people is to be formed from 3 men, 2 women and 4 children. What is the probability that exactly two of chosen people are children?a)13/21b)10/31c)5/21d)10/21e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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