An institute has 8 classes, and each class has 40 students. They will draw 3 students such that each selected student is from a different class. What is the probability that a certain student will be among the selected ones?
Let $A$ denote the student in question.

For $A$ to be among the 3 selected, two independent events must occur simultaneously: 1. $A$'s class must be among the 3 selected classes, 2. $A$ must be the one selected from the 40 students in their class.

1. What is the probability that $A$'s class is among the 3 selected? The number of possible cases is the number of ways to choose 3 from 8, which is $\binom{8}{3}$. The number of favorable cases is the number of groups of three that include $A$'s class with two other classes; this number is $\binom{7}{2}$, since these 2 must be chosen from the remaining 7. Therefore,

$$
v_{1}=\frac{\binom{7}{2}}{\binom{8}{3}}=\frac{7 \cdot 6}{1 \cdot 2}: \frac{8 \cdot 7 \cdot 6}{1 \cdot 2 \cdot 3}=\frac{3}{8}
$$

Accordingly,

2. The probability that $A$ is selected from 40 students is $v_{2}=\frac{1}{40}$.

$$
v=v_{1} v_{2}=\frac{1}{40} \cdot \frac{3}{8}=\frac{3}{320}
$$