Overview

Combinatorics is concerned with defining a finite or discrete mathematical system, and then solving problems relating to the selection and arrangement of numbers or items within that system. A typical problem in combinatorics is to determine the number of possible configurations of a particular type, such as the values that could occur when rolling a pair of dice. Combinatorics has many applications in probability as well as in algebra and geometry.

Background

Combinatorics is an ancient branch of mathematics. In the Rhind Papyrus of Egypt, one of the oldest mathematical texts in existence, the 79th problem asks, "There are seven houses; in each house there are seven cats; each cat kills seven mice; each mouse has eaten seven grains of barley; each grain would have produced seven hekat. What is the sum of all the enumerated things?"

The Rhind...