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I am looking for a rule that would explain whether one would say "those types of problem" vs "those types of problems". I feel that the singular is needed, as there are several types/kinds/categories/sorts of one thing. But we would say "those types of people".

Bryan Garner's Modern American Usage rightly critiques the singular "those kind of problems" and recommends "that kind of problem". But he also accepts "those kinds of problems" and does not suggest putting "problem" in the singular after a plural "those kinds".

In other grammar guides on line I have found examples such as:

"There are a number of different types of student, including independent or dependent, collaborative or competitive and participant or avoidant ones.3

What say ye?