People generally did very well on that homework !
The most common mistakes were in problem 5.19 and problem 5.31 . In 5.19, finding a simple general formula appears to be difficult, so the easiest was to just consider each value of k separately. In problem 5.31, some of you overcounted: i.e. counted a single possibility several times (e.g. in this exercise, the pair (A,B) was the same as (B,A)). It is easy to make such mistakes, always take a moment to check you are really counting distinct arrangements.
As always, remember to always write sentences in plain English explaning your formulas, this will help you (and the grader) understand what you are doing better, and avoid making mistakes.