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In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
- a)266
- b)5040
- c)11760
- d)86400
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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To find the number of ways a committee can be formed from a given set of people, we use the concept of combinations.
Given:
Total number of men = 8
Total number of women = 10
Number of men required in the committee = 5
Number of women required in the committee = 6
We need to find the number of ways to select 5 men out of 8 and 6 women out of 10.
Using the combination formula, the number of ways to select k items out of n items is given by:
C(n, k) = n! / (k! * (n-k)!)
where n! represents the factorial of n.
Solution:
Number of ways to select 5 men out of 8:
C(8, 5) = 8! / (5! * (8-5)!) = (8 * 7 * 6) / (3 * 2 * 1) = 56
Number of ways to select 6 women out of 10:
C(10, 6) = 10! / (6! * (10-6)!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210
To find the total number of ways to form the committee, we need to multiply the number of ways to select men and women together:
Total number of ways = 56 * 210 = 11,760
Therefore, the correct answer is option C) 11,760.
Given:
Total number of men = 8
Total number of women = 10
Number of men required in the committee = 5
Number of women required in the committee = 6
We need to find the number of ways to select 5 men out of 8 and 6 women out of 10.
Using the combination formula, the number of ways to select k items out of n items is given by:
C(n, k) = n! / (k! * (n-k)!)
where n! represents the factorial of n.
Solution:
Number of ways to select 5 men out of 8:
C(8, 5) = 8! / (5! * (8-5)!) = (8 * 7 * 6) / (3 * 2 * 1) = 56
Number of ways to select 6 women out of 10:
C(10, 6) = 10! / (6! * (10-6)!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210
To find the total number of ways to form the committee, we need to multiply the number of ways to select men and women together:
Total number of ways = 56 * 210 = 11,760
Therefore, the correct answer is option C) 11,760.
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In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?a)266b)5040c)11760d)86400e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?a)266b)5040c)11760d)86400e)None of theseCorrect 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 6 women can be formed from 8 men and 10 women?a)266b)5040c)11760d)86400e)None of theseCorrect 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 6 women can be formed from 8 men and 10 women?a)266b)5040c)11760d)86400e)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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