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A committee of 5 is to be formed from 6 boys and 5 girls. The number of ways so that the committee can be formed so that the committee contains at least one boy and one girl having majority of boys is
- a)240
- b)245
- c)250
- d)275
Correct answer is option 'D'. Can you explain this answer?
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A committee of 5 is to be formed from 6 boys and 5 girls. The number o...
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To solve this problem, we can use the concept of combinations.
We want to form a committee of 5 members with at least one boy and one girl.
Step 1: Calculate the total number of ways to form a committee of 5 members from the given 11 candidates.
The total number of ways to select 5 members from 11 candidates is given by the combination formula:
C(11, 5) = 11! / (5! * (11 - 5)!) = 11! / (5! * 6!) = (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1) = 462
Therefore, there are 462 ways to form a committee of 5 members from the given candidates.
Step 2: Calculate the number of ways to form a committee with only boys.
Since there are 6 boys and we need to select 5 members, we can directly use the combination formula:
C(6, 5) = 6! / (5! * (6 - 5)!) = 6! / (5! * 1!) = 6
Therefore, there are 6 ways to form a committee with only boys.
Step 3: Calculate the number of ways to form a committee with only girls.
Since there are 5 girls and we need to select 5 members, we can directly use the combination formula:
C(5, 5) = 5! / (5! * (5 - 5)!) = 5! / (5! * 0!) = 1
Therefore, there is 1 way to form a committee with only girls.
Step 4: Calculate the number of ways to form a committee with at least one boy and one girl.
To find the number of ways to form a committee with at least one boy and one girl, we subtract the number of ways to form a committee with only boys or only girls from the total number of ways.
Number of ways = Total number of ways - Number of ways with only boys - Number of ways with only girls
= 462 - 6 - 1
= 455
Therefore, the number of ways to form a committee with at least one boy and one girl, having a majority of boys, is 455.
We want to form a committee of 5 members with at least one boy and one girl.
Step 1: Calculate the total number of ways to form a committee of 5 members from the given 11 candidates.
The total number of ways to select 5 members from 11 candidates is given by the combination formula:
C(11, 5) = 11! / (5! * (11 - 5)!) = 11! / (5! * 6!) = (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1) = 462
Therefore, there are 462 ways to form a committee of 5 members from the given candidates.
Step 2: Calculate the number of ways to form a committee with only boys.
Since there are 6 boys and we need to select 5 members, we can directly use the combination formula:
C(6, 5) = 6! / (5! * (6 - 5)!) = 6! / (5! * 1!) = 6
Therefore, there are 6 ways to form a committee with only boys.
Step 3: Calculate the number of ways to form a committee with only girls.
Since there are 5 girls and we need to select 5 members, we can directly use the combination formula:
C(5, 5) = 5! / (5! * (5 - 5)!) = 5! / (5! * 0!) = 1
Therefore, there is 1 way to form a committee with only girls.
Step 4: Calculate the number of ways to form a committee with at least one boy and one girl.
To find the number of ways to form a committee with at least one boy and one girl, we subtract the number of ways to form a committee with only boys or only girls from the total number of ways.
Number of ways = Total number of ways - Number of ways with only boys - Number of ways with only girls
= 462 - 6 - 1
= 455
Therefore, the number of ways to form a committee with at least one boy and one girl, having a majority of boys, is 455.
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A committee of 5 is to be formed from 6 boys and 5 girls. The number of ways so that the committee can be formed so that the committee contains at least one boy and one girl having majority of boys isa)240b)245c)250d)275Correct answer is option 'D'. Can you explain this answer?
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A committee of 5 is to be formed from 6 boys and 5 girls. The number of ways so that the committee can be formed so that the committee contains at least one boy and one girl having majority of boys isa)240b)245c)250d)275Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A committee of 5 is to be formed from 6 boys and 5 girls. The number of ways so that the committee can be formed so that the committee contains at least one boy and one girl having majority of boys isa)240b)245c)250d)275Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A committee of 5 is to be formed from 6 boys and 5 girls. The number of ways so that the committee can be formed so that the committee contains at least one boy and one girl having majority of boys isa)240b)245c)250d)275Correct answer is option 'D'. Can you explain this answer?.
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