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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?
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A committee of 7 members is to be formed by selecting numbers at rando...
Forming a Committee from a Pool of Candidates
To form a committee of 7 members by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men, the following steps can be followed:
Determine the Total Number of Ways to Select the Committee
- The total number of ways to select a committee of 7 members from 14 candidates can be calculated using the combination formula:
- C(n, r) = n! / (r!(n-r)!)
- In this case, C(14, 7) = 14! / (7!(14-7)!) = 3432
Selecting Women and Men for the Committee
- To ensure a diverse committee, we can aim to have a balance of women and men.
- We can calculate the number of ways to select 1 woman and 6 men:
- C(5, 1) * C(9, 6) = 5 * 84 = 420 ways
- Similarly, we can calculate the number of ways to select 2 women and 5 men, 3 women and 4 men, and so on.
Determine the Final Committee
- By considering all possible combinations of women and men in the committee, we can determine the final composition of the committee.
- Each combination should be evaluated based on the skills, expertise, and diversity required for the committee's objectives.
By following these steps, a committee of 7 members can be effectively formed from a pool of 14 candidates consisting of 5 women and 9 men, ensuring a balanced and diverse representation.
To form a committee of 7 members by selecting numbers at random from a pool of 14 candidates consisting of 5 women and 9 men, the following steps can be followed:
Determine the Total Number of Ways to Select the Committee
- The total number of ways to select a committee of 7 members from 14 candidates can be calculated using the combination formula:
- C(n, r) = n! / (r!(n-r)!)
- In this case, C(14, 7) = 14! / (7!(14-7)!) = 3432
Selecting Women and Men for the Committee
- To ensure a diverse committee, we can aim to have a balance of women and men.
- We can calculate the number of ways to select 1 woman and 6 men:
- C(5, 1) * C(9, 6) = 5 * 84 = 420 ways
- Similarly, we can calculate the number of ways to select 2 women and 5 men, 3 women and 4 men, and so on.
Determine the Final Committee
- By considering all possible combinations of women and men in the committee, we can determine the final composition of the committee.
- Each combination should be evaluated based on the skills, expertise, and diversity required for the committee's objectives.
By following these steps, a committee of 7 members can be effectively formed from a pool of 14 candidates consisting of 5 women and 9 men, ensuring a balanced and diverse representation.
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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?
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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? 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? 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?.
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? 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? 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?.
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