It's easy to find out how many combinations you can have if you know the total number of items, and the number of items you are combining.
It's a little harder to do that in reverse. This document shows how to find the total number of items if you know how many are combined at a time, and the total number of combinations.
This is a set of notes for the first two chapters of an Abstract Algebra course, following the Hungerford textbook table of contents.
One notable feature is the use of a couple of commands that allow one to show only definitions, or only the examples, etc., and another command that allows one to format examples for making handouts.