Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.  

Combinatorics has several approaches and subfields that include: counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics).

vCalc's Combinatorics library contains equations cutting across several sub-fields of combinatorics.