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(B) committee of $12$ members is to be formed such that women are in majority. Since there are $9$ women and $8$ men,the possible cases for women to b

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$2702$

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(B) committee of $12$ members is to be formed such that women are in majority. Since there are $9$ women and $8$ men,the possible cases for women to be in majority are:Case $I$: $9$ women and $3$ menNumber of ways $= {^9C_9} 	imes {^8C_3} = 1 	imes \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$Case $II$: $8$ women and $4$ menNumber of ways $= {^9C_8} 	imes {^8C_4} = 9 	imes \frac{8 	imes 7 	imes 6 	imes 5}{4 	imes 3 	imes 2 	imes 1} = 9 	imes 70 = 630$Case $III$: $7$ women and $5$ menNumber of ways $= {^9C_7} 	imes {^8C_5} = \frac{9 	imes 8}{2 	imes 1} 	imes \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 36 	imes 56 = 2016$Total number of ways $= 56 + 630 + 2016 = 2702$

$A$ committee of $12$ members is to be formed from $9$ women and $8$ men. The number of committees in which the women are in majority is

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