A committee of 5 members is to be formed from | vedclass

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Question

(B) Total number of ways to select $5$ members from $10$ people ($6$ men + $4$ women) is given by ${}^{10}C_5 = \frac{10 	imes 9 	imes 8 	imes 7

Vedclass · Accepted Answer

$\frac{41}{42}$

Vedclass · Answer

(B) Total number of ways to select $5$ members from $10$ people ($6$ men + $4$ women) is given by ${}^{10}C_5 = \frac{10 	imes 9 	imes 8 	imes 7 	imes 6}{5 	imes 4 	imes 3 	imes 2 	imes 1} = 252$.The number of ways to select a committee with no women (i.e.,all $5$ members are men) is given by ${}^{6}C_5 = 6$.The number of ways to select at least one woman is (Total ways) - (Ways with no women) = $252 - 6 = 246$.Therefore,the required probability is $P = \frac{246}{252} = \frac{41}{42}$.

$A$ committee of $5$ members is to be formed from $6$ men and $4$ women. The probability that at least one woman is present in the committee is

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