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A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee by At most 6 men in the committee.?
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A committee of 7 members is to be formed by selecting numbers at rando...
Probability of selecting at least 3 women and at most 6 men in the committee:
Total number of ways to form a committee:
- The total number of ways to form a committee of 7 members from 14 candidates is given by 14C7.
Number of ways to select at least 3 women:
- To calculate the number of ways to select at least 3 women from 5 candidates, we consider the cases of selecting 3, 4, or 5 women and 4, 3, or 2 men respectively.
Number of ways to select at most 6 men:
- To calculate the number of ways to select at most 6 men from 9 candidates, we consider the cases of selecting 0, 1, 2, 3, 4, 5, or 6 men and 7, 6, 5, 4, 3, 2, or 1 women respectively.
Probability calculation:
- The probability of selecting at least 3 women and at most 6 men in the committee can be calculated by dividing the number of ways to form a committee with at least 3 women and at most 6 men by the total number of ways to form a committee.
Final Answer:
- By calculating the probabilities as mentioned above, we can determine the probability of forming a committee with at least 3 women and at most 6 men from the given pool of candidates.
Total number of ways to form a committee:
- The total number of ways to form a committee of 7 members from 14 candidates is given by 14C7.
Number of ways to select at least 3 women:
- To calculate the number of ways to select at least 3 women from 5 candidates, we consider the cases of selecting 3, 4, or 5 women and 4, 3, or 2 men respectively.
Number of ways to select at most 6 men:
- To calculate the number of ways to select at most 6 men from 9 candidates, we consider the cases of selecting 0, 1, 2, 3, 4, 5, or 6 men and 7, 6, 5, 4, 3, 2, or 1 women respectively.
Probability calculation:
- The probability of selecting at least 3 women and at most 6 men in the committee can be calculated by dividing the number of ways to form a committee with at least 3 women and at most 6 men by the total number of ways to form a committee.
Final Answer:
- By calculating the probabilities as mentioned above, we can determine the probability of forming a committee with at least 3 women and at most 6 men from the given pool of candidates.
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A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee by At most 6 men in the committee.?
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A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee by At most 6 men in the committee.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee by At most 6 men in the committee.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee by At most 6 men in the committee.?.
A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee by At most 6 men in the committee.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee by At most 6 men in the committee.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A committee of 7 members is to be formed by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men. 4) What is the probability that there will be at least 3 women in the committee by At most 6 men in the committee.?.
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