A committee of 7 members is to be formed from | vedclass

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Question

(A) To form a committee of $7$ members with at least $3$ girls from $9$ boys and $4$ girls,we consider the following cases:Case $1$: $3$ girls and $4$

Vedclass · Accepted Answer

$588$

Vedclass · Answer

(A) To form a committee of $7$ members with at least $3$ girls from $9$ boys and $4$ girls,we consider the following cases:Case $1$: $3$ girls and $4$ boys.The number of ways is $^{4}C_{3} 	imes ^{9}C_{4} = 4 	imes \frac{9 	imes 8 	imes 7 	imes 6}{4 	imes 3 	imes 2 	imes 1} = 4 	imes 126 = 504$.Case $2$: $4$ girls and $3$ boys.The number of ways is $^{4}C_{4} 	imes ^{9}C_{3} = 1 	imes \frac{9 	imes 8 	imes 7}{3 	imes 2 	imes 1} = 1 	imes 84 = 84$.Total number of ways $= 504 + 84 = 588$.

$A$ 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 at least $3$ girls?

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