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A committee of 7 has to be formed from 9 boys and 4 girls.In how many ways can this be done when the committee consists of Exactly 3 girls?
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A committee of 7 has to be formed from 9 boys and 4 girls.In how many ...
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A committee of 7 has to be formed from 9 boys and 4 girls.In how many ...
out of 7 persons , we have to select exactly 3 girls . hence, it's clear that remaining 4 persons will be boys .
Now, number of ways taken 4 boys from 9 boys = 9C4
and number of ways taken 3 girls from 4 girls = 4C3
hence, by fundamental principle of counting ,
total number of ways for making the committee = 9C4 × 4C3
= 9!/5!.4! × 4!/3!
= 9×8×7×6/3×2×1
= 9×8×7
= 504 ways
Now, number of ways taken 4 boys from 9 boys = 9C4
and number of ways taken 3 girls from 4 girls = 4C3
hence, by fundamental principle of counting ,
total number of ways for making the committee = 9C4 × 4C3
= 9!/5!.4! × 4!/3!
= 9×8×7×6/3×2×1
= 9×8×7
= 504 ways
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A committee of 7 has to be formed from 9 boys and 4 girls.In how many ...
Formation of Committee with Exactly 3 Girls
To form a committee with exactly 3 girls, we need to select 3 girls out of 4 girls and 4 boys out of 9 boys.
Selection of Girls
- There are 4 girls, and we need to select 3 of them. This can be done in 4C3 ways, which is equal to 4.
Selection of Boys
- There are 9 boys, and we need to select 4 of them. This can be done in 9C4 ways, which is equal to 126.
Total Ways to Form the Committee
- The total number of ways to form the committee with exactly 3 girls is the product of the ways to select girls and boys, which is 4 * 126 = 504 ways.
Therefore, there are 504 ways to form a committee of 7 members with exactly 3 girls from 9 boys and 4 girls.
To form a committee with exactly 3 girls, we need to select 3 girls out of 4 girls and 4 boys out of 9 boys.
Selection of Girls
- There are 4 girls, and we need to select 3 of them. This can be done in 4C3 ways, which is equal to 4.
Selection of Boys
- There are 9 boys, and we need to select 4 of them. This can be done in 9C4 ways, which is equal to 126.
Total Ways to Form the Committee
- The total number of ways to form the committee with exactly 3 girls is the product of the ways to select girls and boys, which is 4 * 126 = 504 ways.
Therefore, there are 504 ways to form a committee of 7 members with exactly 3 girls from 9 boys and 4 girls.
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A committee of 7 has to be formed from 9 boys and 4 girls.In how many ways can this be done when the committee consists of Exactly 3 girls?
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A committee of 7 has to be formed from 9 boys and 4 girls.In how many ways can this be done when the committee consists of Exactly 3 girls? 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 7 has to be formed from 9 boys and 4 girls.In how many ways can this be done when the committee consists of Exactly 3 girls? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A committee of 7 has to be formed from 9 boys and 4 girls.In how many ways can this be done when the committee consists of Exactly 3 girls?.
A committee of 7 has to be formed from 9 boys and 4 girls.In how many ways can this be done when the committee consists of Exactly 3 girls? 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 7 has to be formed from 9 boys and 4 girls.In how many ways can this be done when the committee consists of Exactly 3 girls? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A committee of 7 has to be formed from 9 boys and 4 girls.In how many ways can this be done when the committee consists of Exactly 3 girls?.
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