Out of 3 men,2 women,and 4 children,if 4 peop | vedclass

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(C) Total number of people $= 3 + 2 + 4 = 9$. Number of ways to select $4$ people out of $9$ is $^9C_4 = \frac{9 	imes 8 	imes 7 	imes 6}{4 	imes

Vedclass · Accepted Answer

$10/21$

Vedclass · Answer

(C) Total number of people $= 3 + 2 + 4 = 9$. Number of ways to select $4$ people out of $9$ is $^9C_4 = \frac{9 	imes 8 	imes 7 	imes 6}{4 	imes 3 	imes 2 	imes 1} = 126$. Number of ways to select exactly $2$ children out of $4$ children and $2$ non-children out of the remaining $5$ people ($3$ men $+ 2$ women) is $^4C_2 	imes ^5C_2$. $^4C_2 = \frac{4 	imes 3}{2 	imes 1} = 6$. $^5C_2 = \frac{5 	imes 4}{2 	imes 1} = 10$. Number of favorable outcomes $= 6 	imes 10 = 60$. Required probability $= \frac{60}{126} = \frac{10}{21}$.

Out of $3$ men,$2$ women,and $4$ children,if $4$ people are selected at random,what is the probability that exactly $2$ children are selected?

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