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Combinatorics is that branch of mathematics concerned with counting things.

Combinatorial problems are so named because they are exercises in counting the number of combinations of various objects.

It has been stated that it is the core of the discipline of discrete mathematics.

Also known as

The field of combinatorics is also known as combinatorial analysis.

Also see

  • Results about combinatorics can be found here.

Historical Note

The earliest record of a problem in combinatorics was Plutarch's account of the attempt of Xenocrates of Chalcedon to find the total number of syllables that could be made from the letters of the alphabet.

According to Plutarch, Xenocrates' result was $1,002,000,000,000$ (a myriad-and-twenty times a myriad-myriad).

In modern times, the field of combinatorics was instigated by the investigations of the Chevalier de Méré, along with the analytical work of Blaise Pascal.