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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)More than one of the above
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In how many ways a committee, consisting of 5 men and 6 women can be f...
Total number of ways to form the committee:
- To form a committee of 5 men and 6 women from a total of 8 men and 10 women, we first calculate the number of ways to choose 5 men from 8 men and 6 women from 10 women.
- This can be done using combination formula: nCr = n! / r!(n-r)!, where n is the total number of items, r is the number of items to choose.
Number of ways to choose 5 men:
- 8 men choose 5 men = 8C5 = 8! / 5!(8-5)! = 56 ways.
Number of ways to choose 6 women:
- 10 women choose 6 women = 10C6 = 10! / 6!(10-6)! = 210 ways.
Total number of ways to form the committee:
- Multiply the number of ways to choose men and women: 56 * 210 = 11760 ways.
Therefore, the correct answer is option 'C' - 11760.
- To form a committee of 5 men and 6 women from a total of 8 men and 10 women, we first calculate the number of ways to choose 5 men from 8 men and 6 women from 10 women.
- This can be done using combination formula: nCr = n! / r!(n-r)!, where n is the total number of items, r is the number of items to choose.
Number of ways to choose 5 men:
- 8 men choose 5 men = 8C5 = 8! / 5!(8-5)! = 56 ways.
Number of ways to choose 6 women:
- 10 women choose 6 women = 10C6 = 10! / 6!(10-6)! = 210 ways.
Total number of ways to form the committee:
- Multiply the number of ways to choose men and women: 56 * 210 = 11760 ways.
Therefore, the correct answer is option 'C' - 11760.
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Community Answer
In how many ways a committee, consisting of 5 men and 6 women can be f...
Given:
5 men selected from 8 men
6 women selected from 10 women
5 men selected from 8 men
6 women selected from 10 women
Formula used:
nCr = n!/[r!(n - r)!]
Where n = possible outcome
r = required outcome
nCr = n!/[r!(n - r)!]
Where n = possible outcome
r = required outcome
Calculation:
Ways to select 5 men
8C5 = 8!/[5!(8 - 5)!]
⇒ (6 × 7 × 8)/(3 × 2) = 56
Ways to select 6 women
10C6 = 10!/[6!(10 - 6)!]
⇒ (7 × 8 × 9 × 10)/(4 × 3 × 2) = 210
Ways to select 5 men and 6 women
56 × 210 = 11760
∴ 5 men and 6 women can be selected in 11760 ways.
Ways to select 5 men
8C5 = 8!/[5!(8 - 5)!]
⇒ (6 × 7 × 8)/(3 × 2) = 56
Ways to select 6 women
10C6 = 10!/[6!(10 - 6)!]
⇒ (7 × 8 × 9 × 10)/(4 × 3 × 2) = 210
Ways to select 5 men and 6 women
56 × 210 = 11760
∴ 5 men and 6 women can be selected in 11760 ways.
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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)More than one of the aboveCorrect 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)More than one of the aboveCorrect answer is option 'C'. Can you explain this answer? for SSC CGL 2024 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL 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)More than one of the aboveCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC CGL 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)More than one of the aboveCorrect answer is option 'C'. Can you explain this answer?.
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