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A committee of 7 has to be formed from 9 boys and 4 girls. In

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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:
(i) exactly $3$ girls?
(ii) at least $3$ girls?
(iii) at most $3$ 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:
(i) exactly

3

girls?
(ii) at least

3

girls?
(iii) at most

3

girls?

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

(i) exactly

3

girls

This means you have to choose

3

girls from

4

and

4

boys from

9

to form a committee of

7

. This can be done in

4 C_{3} \times 9 C_{4}

(ii) At least

3

girls

This means girls can either be

3

4

So first choose

3

girls and

4

boys or

4

girls and

3

boys

Total ways =

4 C_{3} \times 9 C_{4}

4 C_{4} \times 9 C_{3}

(iii) At most

3

girls

This means we have to choose

1

2

3

girls

So this can be done in

4 C_{1} \times 9 C_{6}

4 C_{2} \times 9 C_{5}

4 C_{3} \times 9 C_{4}

ways.

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Question Text	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: (i) exactly $3$ girls? (ii) at least $3$ girls? (iii) at most $3$ girls?
Answer Type	Text solution:1
Upvotes	150

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:(i) exactly 3 girls?(ii) at least 3 girls?(iii) at most 3 girls?

Text solutionVerified

Practice questions from similar books

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:
(i) exactly $3$ girls?
(ii) at least $3$ girls?
(iii) at most $3$ girls?