Here is a direct screenshot of the book:
First of all, what does type mean? Does the author mean that the set with $r$ elements can be partitioned into $n$ subsets? Secondly, an $r$ permutation of $n$ elements was previously defined as the number of ways to arrange $r$ out of $n$ elements in a row. How is that different than the permutation that is defined above? The title of the chapter is "Arrangements and Selections with repetitions", so I guess this has something to do with repetitions.
Side note: If the word "type" is not a strictly defined term which I am simply not aware of, what is the benefit of teaching combinatorics with vague terms like this instead of sticking to plain set notation/terminology?