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Is it correct to use a positive quantifier (many, most, a lot of) and a negative verb? For example, is it correct to say, "Many students don't like to study."? Or is it better to say, "Few students like to study."?
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Either way is fine, it depends on what you want the focus to be.
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Both are correct. Which one to use depends on the meaning of the sentence.
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Comments  
Gaga4GrammarIs it correct to use a positive quantifier (many, most, a lot of) and a negative verb?
Those are OK. It's the universal quantifiers (all, both) that cause trouble when they are the subject of a negative verb.

All of them are not here is ambiguous. It's possible to interpret it as either of the following:

Not all of them are here (, but some of them are here).
All of them are absent.

CJ
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