Much, Many, and A Lot of Rules
Is the noun countable or uncountable?
If countable, use "many" in negative sentences and questions.
If uncountable, use "much" in negative sentences and questions.
For both countable and uncountable nouns, we NORMALLY use "a lot of" in positive sentences and questions. But the same rule applies: "much" for uncountable, "many" for countable.