I've encountered following phrase:
a vocabulary of between 10,000 and 15,000 words
Is this phrase correct? Can
of be followed by
between in this case?
Yes, it is grammatical but a little informal. 'of between' looks unnatural because of the two adjacent prepositions. A more formal way of saying it would be:
The informality of the original 'a vocabulary of between...' comes from treating the prepositional phrase 'between X and Y' as an object, as a range. How big is the vocabulary? Somewhere between 10,000 and 15,000. It is a vocabulary of that range, or
There are other instance of adjacent prepositions at the beginning of a prepositional phrase, but they seem to be of a different sort than this 'range' example. There's 'out of' and 'in to' and one could think of 'into' and 'upon' as the same sort. These examples seem to have evolved from reduplication for emphasis.
The phenomenon of a 'phrasal verb' followed by a prepositional phrase is also quite different. "She dashed off to her room.", where the 'off' 'dashed off' is part of the verb.
Perhaps the person asking the original question wonders whether "a vocabulary between 10,000 and 15,000 words" (omitting "of") is sufficient--or indeed preferable to "a vocabulary of between 10,000 and 15,000 words." I frequently see sentences that omit "of" in similar circumstances--for example, "Stores sell them at prices up to $1000," instead of "Stores sell them at prices of up to $1000."
If that's the issue, I would say that including "of" is better than omitting it, on the theory that making an implied preposition explicit is better than requiring readers to infer it.
"... vocabulary of between ..." has 3,850 hits on Google Books. So, we can say that the phrase is correct.
Furthermore, analogous 'structures' (of followed by between) have many hits on Google Books:
The following references are referred to your specific case (vocabulary of between):
Grammar and writing - Page 10, Rebecca Stott, Peter Chapman [→]
The Royal Society of Medicine encyclopedia of children's health - Page 203, Robert Youngson, Royal Society of Medicine (Great Britain) [→]
English Language and Literary Criticism - Page 117, A.s. Kharbe [→]
I don't see a problem. It conveys a coherent idea.
Suppose the writer said, "He has a vocabularly of 10,000 words." That would certainly be a perfectly valid sentence. So the writer wants to indicate a range. He writes, "... a vocabularly of between 10,000 and 15,000 words".
I don't think there's any rule that you can't have two prepositions in a row. (Or if there is, it should be ignored.) How about, "The plane fell FROM ABOVE the clouds"? Where did it fall from? It fell from a place above the clouds.
"I ran TO NEAR exhaustion." I didn't run to exhaustion, but to a state near it.