Probability of random assignment to form pairs

Question

So the question goes:

I have 100 individuals and 100 different buses, and I randomly assigned each individual to sit on a bus (each bus has equal probability of being selected). How many buses are expected to be empty at the end of assignment?

What type of question is this? Does it have a particular name?

Also - how does it differ from calculating how many pairs of people will be sitting on the same bus? E.g. 2 people on a bus = 1 pair, 3 people on a bus is 3 pairs.

Answer 1

each bus has $(1-\frac{1}{100})^{100}\sim\frac{1}{e}$ to be left empty. By linearity of expectaions the answer is $100(1-\frac{1}{100})^{100}\sim\frac{100}{e}$.