From a group of 7 men and 4 ladies,a committe | vedclass

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(B) Total number of ways to select $6$ persons out of $11$ is given by ${}^{11}C_6 = \frac{11 	imes 10 	imes 9 	imes 8 	imes 7 	imes 6}{6 	imes

Vedclass · Accepted Answer

$\frac{5}{11}$

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(B) Total number of ways to select $6$ persons out of $11$ is given by ${}^{11}C_6 = \frac{11 	imes 10 	imes 9 	imes 8 	imes 7 	imes 6}{6 	imes 5 	imes 4 	imes 3 	imes 2 	imes 1} = 462$.To have exactly $2$ ladies in a committee of $6$,we must select $2$ ladies from $4$ and $4$ men from $7$.Number of ways to select $2$ ladies = ${}^4C_2 = \frac{4 	imes 3}{2 	imes 1} = 6$.Number of ways to select $4$ men = ${}^7C_4 = {}^7C_3 = \frac{7 	imes 6 	imes 5}{3 	imes 2 	imes 1} = 35$.Total favorable ways = ${}^4C_2 	imes {}^7C_4 = 6 	imes 35 = 210$.Probability = $\frac{	ext{Favorable ways}}{	ext{Total ways}} = \frac{210}{462}$.Simplifying the fraction: $\frac{210 \div 42}{462 \div 42} = \frac{5}{11}$.

From a group of $7$ men and $4$ ladies,a committee of $6$ persons is formed. What is the probability that the committee contains exactly $2$ ladies?

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