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In how many ways a committee consisting of 5 men and 3 women, can be chosen from 9 men and 12 women.
- a)12459
- b)75200
- c)27720
- d)18920
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In how many ways a committee consisting of 5 men and 3 women, can be c...
Choose 5 men out of 9 men = 9C5 ways = 126 ways
Choose 3 women out of 12 women = 12C3 ways = 220 ways
The committee can be chosen in 27720 ways
Most Upvoted Answer
In how many ways a committee consisting of 5 men and 3 women, can be c...
Choose 5 men out of 9 men = 9C5 ways = 126 ways
Choose 3 women out of 12 women = 12C3 ways = 220 ways
The committee can be chosen in 27720 ways
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Community Answer
In how many ways a committee consisting of 5 men and 3 women, can be c...
Given:
- Total number of men = 9
- Total number of women = 12
- Number of men to be selected = 5
- Number of women to be selected = 3
We need to find the number of ways a committee can be chosen from these men and women.
To solve this problem, we can use the concept of combinations.
1. Selection of men:
Since we need to choose 5 men from a total of 9 men, we can use the combination formula to calculate the number of ways to select the men:
C(9, 5) = 9! / (5!(9-5)!) = 9! / (5!4!) = (9 * 8 * 7 * 6 * 5!) / (5! * 4 * 3 * 2 * 1) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 9 * 2 * 7 = 126
Therefore, there are 126 ways to select the 5 men.
2. Selection of women:
Similarly, since we need to choose 3 women from a total of 12 women, we can use the combination formula to calculate the number of ways to select the women:
C(12, 3) = 12! / (3!(12-3)!) = 12! / (3!9!) = (12 * 11 * 10 * 9!) / (3! * 9!) = (12 * 11 * 10) / (3 * 2 * 1) = 220
Therefore, there are 220 ways to select the 3 women.
3. Total number of ways:
To find the total number of ways to select the committee consisting of 5 men and 3 women, we multiply the number of ways to select the men and the number of ways to select the women:
Total number of ways = 126 * 220 = 27720
Therefore, the correct answer is option 'C', 27720.
- Total number of men = 9
- Total number of women = 12
- Number of men to be selected = 5
- Number of women to be selected = 3
We need to find the number of ways a committee can be chosen from these men and women.
To solve this problem, we can use the concept of combinations.
1. Selection of men:
Since we need to choose 5 men from a total of 9 men, we can use the combination formula to calculate the number of ways to select the men:
C(9, 5) = 9! / (5!(9-5)!) = 9! / (5!4!) = (9 * 8 * 7 * 6 * 5!) / (5! * 4 * 3 * 2 * 1) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 9 * 2 * 7 = 126
Therefore, there are 126 ways to select the 5 men.
2. Selection of women:
Similarly, since we need to choose 3 women from a total of 12 women, we can use the combination formula to calculate the number of ways to select the women:
C(12, 3) = 12! / (3!(12-3)!) = 12! / (3!9!) = (12 * 11 * 10 * 9!) / (3! * 9!) = (12 * 11 * 10) / (3 * 2 * 1) = 220
Therefore, there are 220 ways to select the 3 women.
3. Total number of ways:
To find the total number of ways to select the committee consisting of 5 men and 3 women, we multiply the number of ways to select the men and the number of ways to select the women:
Total number of ways = 126 * 220 = 27720
Therefore, the correct answer is option 'C', 27720.
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In how many ways a committee consisting of 5 men and 3 women, can be chosen from 9 men and 12 women.a)12459b)75200c)27720d)18920Correct answer is option 'C'. Can you explain this answer?
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In how many ways a committee consisting of 5 men and 3 women, can be chosen from 9 men and 12 women.a)12459b)75200c)27720d)18920Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In how many ways a committee consisting of 5 men and 3 women, can be chosen from 9 men and 12 women.a)12459b)75200c)27720d)18920Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways a committee consisting of 5 men and 3 women, can be chosen from 9 men and 12 women.a)12459b)75200c)27720d)18920Correct answer is option 'C'. Can you explain this answer?.
In how many ways a committee consisting of 5 men and 3 women, can be chosen from 9 men and 12 women.a)12459b)75200c)27720d)18920Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about In how many ways a committee consisting of 5 men and 3 women, can be chosen from 9 men and 12 women.a)12459b)75200c)27720d)18920Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways a committee consisting of 5 men and 3 women, can be chosen from 9 men and 12 women.a)12459b)75200c)27720d)18920Correct answer is option 'C'. Can you explain this answer?.
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