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Question 3:
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?
A committee of 7 has to be formed from 9 boys and 4 girls.
Since exactly 3 girls are to be there in every committee, each committee must consist of (7 – 3) = 4 boys only.
Thus, in this case, required number of ways = 
(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
ways.
4 girls and 3 boys can be selected in 
ways.
Therefore, in this case, required number of 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
3 girls and 4 boys can be selected in 
ways.
2 girls and 5 boys can be selected in 
ways.
1 girl and 6 boys can be selected in 
ways.
No girl and 7 boys can be selected in 
ways.
Therefore, in this case, required number of ways
