Question

Four persons are to be chosen at random from a group of $3$men, $2$ women and $4$ children. Find the probability of selecting.
(i) $1$men, $1$ women and $2$ children,
(ii) exactly, $2$ children,
(iii) $2$ women.

Answer 1

$\left(1\right)$ Probability $=\frac{1}{3}\times \frac{1}{2}\times \frac{2}{4}=\frac{1}{12}$

$\left(2\right)$ $\frac{{}^4{C}_2}{{}^9{C}_2}=\frac{4!\times 2!\times 7!}{2!\times 2!\times 9!}=\frac{1}{6}$

$\left(3\right)$ $\frac{{}^2{C}_2}{{}^9{C}_2}=\frac{2!\times 7!}{9!}=\frac{1}{36}$