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 ?

• A. $\frac{21}{46}$
• B. $\frac{25}{117}$
• C. $\frac{1}{50}$
• D. $\frac{3}{25}$

Answer 1

Answer: (A)

$\frac{21}{46}$

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 $25$

$={{25}_C}_3$

$=\frac{25!}{21!3!}$

$=\frac{25\times 24\times 23\times 22\times 21!}{21!\times 3\times 2}$

$=25\times 4\times 23\times 22\times 21=2300$

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

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

$=1050$

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