Q:

Arranging textbooks on 3 shelves

Suppose I have 13 textbooks that I want to place on 3 shelves. How many ways can I arrange my textbooks if order does not matter?  
They say that this is equivalent to counting number of non-negative solutions to
$$x_1 + x_2 + x_3 = 13$$
However, why is this? If order does not matter, then something like $x_1 = 13, x_2 = 0 , x_3 = 0$ is the same solution as $x_1 = 0, x_2 = 13, x_3 = 0$.
Doesn't that first equation count number of solutions when we consider those two cases as different?

A:

"Order does not matter" refers to the books, not the shelves. Then all books may be considered as identical, and the given argument applies.

