[ Discrete distribution ] $[$ Equations in integers $]$

In a class of 25 children, two are randomly chosen for duty. The probability that both duty students will be boys is $3 / 25$.

How many girls are in the class

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Let there be $n$ boys in the class, then the number of ways to choose an ordered pair of duty students from them is $n(n-1)$, the number of ways to choose an ordered pair from the entire class is $25 \cdot 24$. Therefore, the probability that two boys will be chosen is $n(n-1):(25 \cdot 24)=3 / 25$. Hence, $n(n-1)=72=9 \cdot 8$. Therefore, $n=9$, which means there are 9 boys and 16 girls in the class.

## Answer

16 girls.