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?

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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...
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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 inways. 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 read less
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