Combinatorics is perhaps most simply defined as the science of counting. ... Combinatorics is, arguably, the most difficult subject in mathematics, which some attribute to the fact that it deals with discrete phenomena as opposed to continuous phenomena, the latter being usually more regular and well behaved.

Why combinatorics is so hard?

In short, combinatorics is difficult because there is no easy, ready-made algorithm for counting things fast. You need to identify patterns/regularities offered by the particular problem at hand, and exploit them in a clever way to break down the big counting problem into smaller counting problems.

Do you need calculus for combinatorics?

No. Many pure math classes require no (or very little) calculus. Abstract algebra, number theory, combinatorics, and graph theory certainly fall into this category. ... If you want to study graph theory or combinatorics [1], then calculus will be pretty much useless to you, and you'll naturally go years without using it.