I don't meant to turn into TrueTears and give you a full blow-by-blow account of probability and statistics, but to my eye that looks like a Hypergeometric distribution which is used for selection without replacement. While you don't need to know what a hypergeometric sequence is (esp. so close to the exam!) but it's based on combinatorics as others have stated. You can think of it as a quicker alternative to drawing out a tree diagram.
Essentially:
Take a sample of 2 from a group of 8. You can't expect the probability to remain the same since the probabilities will significantly change between selections! You can draw out a tree diagram and you'll find:
You'll notice when we sum these two together you get to the same probability as the worked solution,
A binomial distribution could not have been used because the probability of success/failure changes for each 'step' in the tree diagram.
For a larger population when you select a few cars for a sample you can do the same thing of changing the probabilities as each item is selected and drag a tree diagram etc. On the other hand for very large samples, e.g. 1000, then 500/1000 is approximately 499/900. So we can make the assumption that the probability is constant even though selecting a sample is technically a non-replacement process meaning we can use a binomial distribution.
However, typically in Methods it's a clear cut case where they tell you the population probability is P (this is almost always the case for statistics!!).
It's only when they tell you the population size is Y and a sample of size of X where X and Y are similar magnitude you need to think about creating a tree diagram/using combinatorics.