In high school, when we talked about "combinatorics," we solely meant "mathematics of choice." For instance:
- There are 10 people who want to sit around a table. In how many ways is this possible?
- We have 50 balls and 20 boxes. In how many ways can we distribute balls into the boxes?
- There are 10 apples and 5 oranges. In how many ways can we select 7 fruits?
I did have this certain wrong view of combinatorics unless I read about combinatorial objects (lists, sets, graphs, etc.) and combinatorial proofs. I tried reading several sources (Wikipedia, books, papers), but still don't have a clear understanding of when something is called combinatorial.
Could you please elaborate it?