Answer : Option C

Explanation :

Let S be the sample space.
n(S) = Total number of ways of selecting 3 students from 25 students = ²⁵C₃
Let E = Event of selecting 1 girl and 2 boys
n(E) = Number of ways of selecting 1 girl and 2 boys
15 boys and 10 girls are there in a class.
We need to select 2 boys from 15 boys and 1 girl from 10 girls
Number of ways in which this can be done = ¹⁵C₂ × ¹⁰C₁
Hence n(E) = ¹⁵C₂ × ¹⁰C₁

$MF#% \text{P(E) = }\dfrac{\text{n(E)}}{\text{n(S)}}$MF#%$MF#% = \dfrac{15_{C_2} \times 10_{C_1}}{25_{C_3}}$MF#%

$MF#%\begin{align}&=\dfrac{\left(\dfrac{15 \times 14 }{2 \times1}\right) \times 10}{\left(\dfrac{25 \times 24 \times 23}{3 \times 2 \times1}\right)}
= \dfrac{15 \times 14 \times 10}{\left(\dfrac{25 \times 24 \times 23}{3}\right)}
= \dfrac{15 \times 14 \times 10}{25 \times 8 \times 23}
= \dfrac{3 \times 14 \times 10}{5 \times 8 \times 23}\\\\\\\\
&= \dfrac{3 \times 14 \times 2}{8 \times 23}
= \dfrac{3 \times 14 }{4 \times 23}
= \dfrac{3 \times 7}{2 \times 23}
= \dfrac{21}{46}\end{align} $MF#%