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: Option A

Let S be the sample space and E be the event of selecting 1 girl and 2 boys
Then, n(S) = Number ways of selecting 3 students out of 25
$$\begin{array}{rl}& ={}^{25}{C}_3\\ & =\frac{25\times 24\times 23}{3\times 2\times 1}\\ & =2300\\ & n\left(E\right)={}^{10}{C}_1{\times }^{15}{C}_2\\ & =10\times \frac{15\times 14}{2\times 1}\\ & =1050\\ & \therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{1050}{2300}=\frac{21}{46}\end{array}$$