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) at least 3 girls? 

(iii) almost 3 girls?

Answer 1

(i) There are 9 boys and 4 girls. We have to select exactly 3 girls out of 4 girls and 4 boys out of 9 boys.

∴  Number of ways of selection 

(ii) We have to select at least 3 girls. So the committee consists of 3 girls and 4 boys or 4 girls and 3 boys. 

∴ Number of ways of selection = ⁴C₃ × ⁹C₄ + ⁴C₄ × ⁹C₃ 

(iii) We have to select at most 3 girls. So the committee consists of no girl and 7 boys or 1 girl and 6 boys or 2 girls and 5 boys or 3 girls and 4 boys.

∴ Number of ways of selection