Question

In a class, there are $15$ boys and $10$ girls. Three students are selected at random. The probability that $1$ girl and $2$ boys are selected, is :

Answer 1

Let $S$ be the sample space and E be the event of selecting $1$ girl and $2$ boys.

Then, $n\left(S\right)=$ Number ways of selecting $3$ students out of $25$

$={{25}_C}_3$

$=\frac{25!}{22!3!}$

$=\frac{25\times 24\times 23\times 22!}{22!\times 3\times 2}$

$=25\times 4\times 23=2300$

$n\left(E\right)=({{10}_C}_1\times {{15}_C}_2)$

$=[10\times \frac{15\times 14}{2\times 1}]$

$=1050$

$\therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{1050}{2300}=\frac{21}{46}$