A group of 3 is selected at random from 3 men | vedclass

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(C) Total number of people = $3 + 2 + 4 = 9$.We need to select a group of $3$ people from $9$.The total number of ways to select $3$ people is $n = \b

Vedclass · Accepted Answer

$\frac{5}{21}$

Vedclass · Answer

(C) Total number of people = $3 + 2 + 4 = 9$.We need to select a group of $3$ people from $9$.The total number of ways to select $3$ people is $n = \binom{9}{3} = \frac{9 	imes 8 	imes 7}{3 	imes 2 	imes 1} = 84$.We want exactly $2$ children in the group of $3$.This means we select $2$ children from $4$ children and $1$ person from the remaining $5$ people ($3$ men + $2$ women).The number of favorable ways is $r = \binom{4}{2} 	imes \binom{5}{1} = 6 	imes 5 = 30$.The probability $P(A) = \frac{r}{n} = \frac{30}{84} = \frac{5}{14}$.

$A$ group of $3$ is selected at random from $3$ men,$2$ women,and $4$ children. What is the probability that the group contains exactly $2$ children?

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