What is a Combinatorial Object?
Combinatorial objects are everywhere! How many ways are there to make change for $1 using unlimited numbers of coins of all denominations? Each way is a combinatorial object known as a numerical partition. How many ways are there for Alice, Bob, and Carol to line up at the box office at a theatre? Each way is a combinatorial object known as a permutation. How many 5-card poker hands are there with a pair of aces; what is the probability of getting such a hand? To answer this question you need to know about combinatorial objects known as combinations. But what is a combinatorial object? It’s actually very difficult to define. Kind of like love: you know it when you see it, but it’s hard to explain. The main feature of such objects is that there is only a finite number of any particular type. There is only a finite number of ways for persons to order themselves in line at a theatre, only a finite number of ways to make change for a dollar. On the other hand, temperature does not take on
