11. There are 25 children in the class. Two are chosen at random for duty. The probability that both duty students will be boys is $\frac{3}{25}$. How many girls are in the class?
# Solution.

Let there be $n$ boys in the class, then the number of ways to choose two duty students from them is $\frac{n(n-1)}{2}$, the number of ways to choose two duty students from the entire class is $25 \cdot 24$. The ratio of the two obtained fractions, i.e., $\frac{n(n-1)}{25 \cdot 24}$. It is also equal to $\frac{3}{25}$ according to the condition. We get the quadratic equation $n^{2}-n-72=0$. Its roots are -8 and 9. Only the positive root fits us, i.e., there are 9 boys in the class, and, consequently, 16 girls.

Answer: 16.