As we all agree on, types when plural, always comes after "of" a plural noun.. Like types of cars : meaning different classes of cars. My question here is : when I want to address one type of the "types" of cars, why should make "car" not cars to be this type of car, not cars?? Another example : we have different types of students, but this type of students is the hardest to deal with? As here I address one type of "different types " as the prepositional phrase "of students"works as an adjective for types or"type"
In order to give Google NGrams more data to work with, I use thing(s) at the ends of phrases, rather than car(s) or student(s). Google NGrams shows that the following four types of plural are used in this order of frequency (most frequent at the top):
- these types of things
- these type of things
- this type of things
- these types of thing
I got the same order when using kind instead of type; the order is
- these kinds of things
- these kind of things
- this kind of things
- these kinds of thing
In both cases, the phrase with the adjective and both nouns all plural is the most prevalent usage by far.