1. There are 100 students who want to sign up for the class Introduction to Acting. There are three class sections for Introduction to Acting, each of which will fit exactly 20 students. The 100 students, including Alex and Zhu, are put in a lottery, and 60 of them are randomly selected to fill up the classes. What is the probability that Alex and Zhu end up getting into the same section for the class?
Answer: $19 / 165$ There is a $\frac{60}{100}=\frac{3}{5}$ chance that Alex is in the class. If Alex is in the class, the probability that Zhu is in his section is $\frac{19}{99}$. So the answer is $\frac{3}{5} \cdot \frac{19}{99}=\frac{19}{165}$.