ABSTRACT
This is the start of our four-chapter-long focus on combinatorics, and it is jampacked with (related-to-each-other) ideas! Combinatorics is the science of counting. We will begin by considering the number of ways to choose some objects from a larger pile of objects. This will lead us to investigate the links between choosing objects, Pascal’s triangle, and powers of (x + y). (At first glance, these don’t seem to have anything to do with each other . . . surprise!) We will also see how these ideas tie in to the factorial function (n!) and how factorials relate to arranging objects in different orders. As before, every exploration is followed by reinforcing material in a subsequent section.
