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## 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...

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