I wouldn't use the article, because you are talking about the general thing. On the other hand, if you say "a number of cars", you are referring to a small amount of cars (the same as "a few"), while "the number of cars" refers to the exact number of cars. If someone has got a different opinion, please advise. Greetings!

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Go with 'the,' generally. "The number of cars." For example, without public transportation, the total number of cars on the road in the city is 1000. With public transportation, 'the number of cars' is reduced to 800. You can also say 'a number of cars' but it has a slightly different meaning/operation...i.e. from the total number of cars, 'a quantity of cars' will no longer be on the road due to the usage of public transport.You would maybe need to say 'it will reduce a number of cars FROM the road'...sounds a bit better that way.

All can be correct depending on the meaning you want to convey. 1. the number of cars: the overall quantity of cars present on the roads can be reduced. 2. a number of cars: an unspecified quantity of cars can be reduced (synonymous of: “some/a few cars”) 3. number of cars: a more general statement. Can reduce the overall quantity of cars on the roads, without specifying whether it's all cars or just a small portion.