The mathimatical discipline which attempts to answer "how many" questions (without actually having to count).

Combinatorics is a branch of mathematics that studies collections (usually finite) of objects that satisfy specified criteria. In particular, it is concerned with "counting" the objects in those collections (enumerative combinatorics), with deciding when the criteria can be met, with constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), with finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and with finding algebraic structures these objects may have (algebraic combinatorics).

The science that studies the numbers of different combinations, which are groupings of numbers. Combinatorics is often part of the study of probability and statistics.