3.1, 3.2 due on 10/10

Difficult
I understood most of section 3.1 because a lot of it I've learned before. However, the following definition confused me: "a number n (say) of objects or things are to be divided or distributed into r classes or groups." In the example following this definition, there wasn't any reference to this definition or what n and r correlate to in a given problem. In section 3.2, this was cleared up since theorems (1) and (2) gave better explanations of how we can split n objects into r groups. Although, theorem (3) gave me some trouble because I don't quite follow the proof and I'm not sure what a multinomial coefficient is.
Reflective
The example in section 3.2 really helped me understand how the multinomial coefficient works, even though I'm still not sure what it is. It seems to me if you have Mn (x, y, z) then that means there are n total objects, with x number of objects of type 1, y number of objects of type 2, and z number of objects of type 3. The reason you divide n! by the product of (x! y! z!) is in order to have no repeats in the permutations.