Probability of at least one empty subway car

Question

I have the following task: there is a subway train with 4 empty cars and 15 passengers getting in it. What is the probability that at least one car will be empty?

Answer 1

Hint:

Let $E_i$ denote the event that car $i$ stays empty.

Then to be found is:$$P(E_1\cup E_2\cup E_3\cup E_4)$$ Apply the principle of inclusion/exclusion.