Question

Four persons are selected at random out of 3 men, 2 women and 4 children. The probability that there are exactly 2 children in the selection is

• A. $\frac{11}{21}$
• B. $\frac{9}{21}$
• C. $\frac{10}{21}$
• D. none of these

Answer 1

The correct option is C

$\frac{10}{21}$

There are nine persons (three men, two women and four children) out of which four persons can be selected in ${}^9{C}_4=126$ ways.

$\therefore$ Total number of elementary events = 126 Exactly two children means selecting two children and two other people from three men and two women.

This can be done in ${}^4{C}_2{\times }^5{C}_2$ ways

$\therefore$ Favourable number of elementary events

${=}^4{C}_2{\times }^5{C}_2=60$

So, required probability $=\frac{60}{126}=\frac{10}{21}$