Comment by getnormality

I think the best single thing for programmers to know about combinatorics is combinatorial data structures. If you have a collection of objects and you need to iterate over all possible combinations, subsets, or permutations of that collection, libraries like Python's itertools do this for you. The resulting code will be clearer, more concise, and more reliable than if you reinvent the wheel with some hand-coded rat's nest of loops.

If you need to know how long that's going to take, you'll need to know some enumerative combinatorics.