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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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