【Example 10】The library has received $n$ new types of books, with $m$ copies of each type. Now, $r(n \leqslant$ $r \leqslant m$ ) people go to borrow books, with each person limited to borrowing 1 book. How many ways are there for each type of new book to be borrowed?
Let's conceptualize this problem as a "ball-into-box" problem: $r$ people are considered as $r$ distinct balls, and $n$ types of books are considered as $n$ distinct boxes. If a ball is placed into a box, it is equivalent to a person borrowing a book of that type. Given $n \leqslant r \leqslant m$, this can also be seen as a ball-into-box problem with unlimited capacity. If every type of book is borrowed by someone, it is equivalent to no box being empty. Therefore, according to the result of Example 9, there are $f(r, n)$ ways for this to happen.