Whether it is the pigeonhole principle?

Question

I had a question, and I am just wondering if it is a question that involves combinations/permutations or the pigeonhole principle.

In a class are $20$ students. What is the probability that at least three of these students have thee same zodiac sign (there are 12 zodiac signs in total)?

I was seeing if anyone would like to explain to me, on how to determine if a question involves combination/permutation or the pigeonhole principle?

Thanks.

Answer 1

Pigeonhole and combination both will be used here. To find answer one would like to discard the case when 1) all are of different sign & 2) some sign has two people and no sign has 3 or more. Pigeonhole says case 1) is not possible and to count possibilities of case 2) one needs combination.