Number of girls = 4

Number of boys = 9

(i) Since the committee has to consists exactly 3 girls, the committee can consist of 3 girls and 4 boys.

∴ 3 girls out of 4 can be selected in ^{4}C_{3} ways out of 4 boys out of 9 can be selected in ^{9}C_{4} ways

∴ Required number of ways = ^{4}C_{3} x ^{9}C_{4}

= 4 x (9 x 8 x 7 x 6)/(4 x 3 x 2 x 1) = 504

(ii) Since the committee has to consist at least 3 girls, the committee can consists of

(a) 3 girls and 4 boys

(b) 4 girls and 3 boys

(a) 3 girls and 4 boys can be selected in = ^{4}C_{3} x ^{9}C_{4} ways

(b) 4 girls and 3 boys can be selected in ^{4}C_{4} x ^{9}C_{3} ways

∴ Required number of ways = ^{4}C_{3} x ^{9}C_{4 }+ ^{4}C_{4} x ^{9}C_{3}

= 4 x 126 + 1 x 84 = 504 + 84 = 588

(iii) In this case, commitee may consists of 3 girls, 2 girls ,1 girl or no girl.