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 ${}^{10}C_5 = \frac{10 	imes 9 	imes 8 	imes 7 	imes 6}{5

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 ${}^{10}C_5 = \frac{10 	imes 9 	imes 8 	imes 7 	imes 6}{5 	imes 4 	imes 3 	imes 2 	imes 1} = 252$.The number of ways to select a committee with no women (i.e.,all $5$ members are men) is ${}^6C_5 = 6$.The number of ways to select at least one woman is (Total ways) - (Ways with no women) = $252 - 6 = 246$.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. What is the probability that the committee contains at least one woman?

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