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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...
Calculating the Probability of Selecting the Committee
Determining the Total Number of Ways to Select the Committee
There are a total of 14 candidates, and we need to select a committee of 7 members. Therefore, the total number of ways to select the committee is given by the combination formula C(14, 7) = 3003.
Determining the Number of Ways to Select at least 3 women and at most 6 men
We need to calculate the number of ways to select at least 3 women and at most 6 men for the committee.
Calculating the Number of Ways to Select 3 Women
There are 5 women in the pool, and we need to select 3 of them. This can be done in C(5, 3) = 10 ways.
Calculating the Number of Ways to Select at most 6 Men
There are 9 men in the pool, and we need to select at most 6 of them. This can be done in C(9, 0) + C(9, 1) + C(9, 2) + C(9, 3) + C(9, 4) + C(9, 5) + C(9, 6) = 502 ways.
Calculating the Total Number of Ways to Select the Committee with the Given Criteria
The total number of ways to select a committee with at least 3 women and at most 6 men is given by multiplying the number of ways to select 3 women and at most 6 men, i.e., 10 * 502 = 5020 ways.
Calculating the Probability
To calculate the probability of selecting a committee with at least 3 women and at most 6 men, we divide the total number of ways to select such a committee by the total number of ways to select any committee, i.e., 5020 / 3003 ≈ 0.6667.
Therefore, the probability that there will be at least 3 women in the committee and at most 6 men is approximately 0.6667 or 66.67%.
Determining the Total Number of Ways to Select the Committee
There are a total of 14 candidates, and we need to select a committee of 7 members. Therefore, the total number of ways to select the committee is given by the combination formula C(14, 7) = 3003.
Determining the Number of Ways to Select at least 3 women and at most 6 men
We need to calculate the number of ways to select at least 3 women and at most 6 men for the committee.
Calculating the Number of Ways to Select 3 Women
There are 5 women in the pool, and we need to select 3 of them. This can be done in C(5, 3) = 10 ways.
Calculating the Number of Ways to Select at most 6 Men
There are 9 men in the pool, and we need to select at most 6 of them. This can be done in C(9, 0) + C(9, 1) + C(9, 2) + C(9, 3) + C(9, 4) + C(9, 5) + C(9, 6) = 502 ways.
Calculating the Total Number of Ways to Select the Committee with the Given Criteria
The total number of ways to select a committee with at least 3 women and at most 6 men is given by multiplying the number of ways to select 3 women and at most 6 men, i.e., 10 * 502 = 5020 ways.
Calculating the Probability
To calculate the probability of selecting a committee with at least 3 women and at most 6 men, we divide the total number of ways to select such a committee by the total number of ways to select any committee, i.e., 5020 / 3003 ≈ 0.6667.
Therefore, the probability that there will be at least 3 women in the committee and at most 6 men is approximately 0.6667 or 66.67%.
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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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