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

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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

(i) Exactly 3 girls ?

(ii) atleast 3 girls ?

(iii)atmost 3 girls

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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 4C3 ways out of 4 boys out of 9 can be selected in 9C4 ways

∴ Required number of ways = 4C3 x 9C4

= 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 = 4C3 x 9C4 ways

(b) 4 girls and 3 boys can be selected in 4C4 x 9C3 ways

∴ Required number of ways = 4C3 x 9C4C4 x 9C3

= 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.