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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: - CBSE (Arts) Class 11 - Mathematics

ConceptConcept of Combinations

#### Question

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) atleast 3 girls?

(iii) atmost 3 girls?

#### Solution

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

i) Since exactly 3 girls are to be there in every committee, each committee must consist of (7 – 3) = 4 boys only.

(ii) Since at least 3 girls are to be there in every committee, the committee can consist of

(a) 3 girls and 4 boys or (b) 4 girls and 3 boys

3 girls and 4 boys can be selected in ""^4C_3 xx ""^9C_4 ways.

4 girls and 3 boys can be selected in ""^4C_4 xx  ""^9C_3 ways.

(iii) Since atmost 3 girls are to be there in every committee, the committee can consist of

(a) 3 girls and 4 boys (b) 2 girls and 5 boys

(c) 1 girl and 6 boys (d) No girl and 7 boys

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 7: Permutations and Combinations
Q: 3 | Page no. 156

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Solution 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: Concept: Concept of Combinations.
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