The number of ways in which a committee of 6 | vedclass

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Question

(A) To form a committee of $6$ members from $8$ gentlemen and $4$ ladies such that it contains at least $3$ ladies,we consider the following cases:Cas

Vedclass · Accepted Answer

$252$

Vedclass · Answer

(A) To form a committee of $6$ members from $8$ gentlemen and $4$ ladies such that it contains at least $3$ ladies,we consider the following cases:Case $1$: The committee contains $3$ ladies and $3$ gentlemen.The number of ways is given by $\binom{4}{3} 	imes \binom{8}{3} = 4 	imes \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 4 	imes 56 = 224$.Case $2$: The committee contains $4$ ladies and $2$ gentlemen.The number of ways is given by $\binom{4}{4} 	imes \binom{8}{2} = 1 	imes \frac{8 	imes 7}{2 	imes 1} = 1 	imes 28 = 28$.Total number of ways = $224 + 28 = 252$.

The number of ways in which a committee of $6$ members can be formed from $8$ gentlemen and $4$ ladies so that the committee contains at least $3$ ladies is:

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