If a committee of 10 members is to be formed | vedclass

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(D) To form a committee of $10$ members where men are in majority,the number of men must be greater than the number of women. Since the total members

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$595$

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(D) To form a committee of $10$ members where men are in majority,the number of men must be greater than the number of women. Since the total members are $10$,the possible cases for (men,women) are $(6, 4), (7, 3), (8, 2)$.Number of ways = $^8C_6 	imes ^6C_4 + ^8C_7 	imes ^6C_3 + ^8C_8 	imes ^6C_2$.Calculating each term:$^8C_6 	imes ^6C_4 = 28 	imes 15 = 420$.$^8C_7 	imes ^6C_3 = 8 	imes 20 = 160$.$^8C_8 	imes ^6C_2 = 1 	imes 15 = 15$.Total ways = $420 + 160 + 15 = 595$.

If a committee of $10$ members is to be formed from $8$ men and $6$ women,then the number of different possible committees in which the men are in majority is

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