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(A) committee of $7$ members is to be formed from $9$ boys and $4$ girls. Since the committee must contain exactly $3$ girls,the number of boys requir

Vedclass · Accepted Answer

$504$

Vedclass · Answer

(A) committee of $7$ members is to be formed from $9$ boys and $4$ girls. Since the committee must contain exactly $3$ girls,the number of boys required is $7 - 3 = 4$ boys. The number of ways to select $3$ girls from $4$ is given by $^{4}C_{3}$. The number of ways to select $4$ boys from $9$ is given by $^{9}C_{4}$. Total number of ways $= ^{4}C_{3} 	imes ^{9}C_{4}$. $^{4}C_{3} = \frac{4!}{3!1!} = 4$. $^{9}C_{4} = \frac{9 	imes 8 	imes 7 	imes 6}{4 	imes 3 	imes 2 	imes 1} = 126$. Total ways $= 4 	imes 126 = 504$.

$A$ committee of $7$ members is to be formed from $9$ boys and $4$ girls. In how many ways can this be done if the committee must consist of exactly $3$ girls?

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