Combinatorics

Abstract

In this first chapter we will be concerned with problems that are part of classical combinatorics and are based on determining the number of configurations with given properties. The problems in this chapter mainly describe “practical” situations (such as the distribution of cards among different players), that is, the relevant variables are mathematically not sufficiently well formulated. As we begin with the solution of a problem it is therefore important to make sure we know which of the resulting configurations we consider distinct. (In the example of a card game it is normally irrelevant in which order a player is dealt his cards). Our main tool in formalizing these concrete situations will be the notion of an ordered k-triple, with which the reader will already be familiar. At this point we simply note that two k-tuples (a ₁, a ₂,..., a _k ) and (b ₁, b ₂,..., b _k ) are considered equal if and only if the equalities a _l = b ₁, a ₂ = b ₂,..., a _k = b _k are satisfied.