I have always thought that the latter: Cars sale, is incorrect; yet Google returns almost the same number of results for both!

My concern is about Rule extraction and Rules extraction to be precise; for a Chapter title!

P.S. Clearly, we are selling many cars (or extracting many rules); not one!

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    Google return results isn't always a good metric. When I checked, many of the hits for cars sale point to websites that say "USED CARS FOR SALE". – J.R. Jul 20 '13 at 18:03
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    If you're confident enough in your ability to write a book, you shouldn't need us to tell you what you want to say. – Robusto Jul 20 '13 at 18:13
  • If you have a toy car based on the movie "Cars," it's a "Cars car." – Ben Crowell Aug 17 '13 at 1:46

In your examples, car and rule are noun adjuncts: nouns used as adjectives. Wikipedia notes:

Noun adjuncts were traditionally mostly singular (e.g. "trouser press") except when there were lexical restrictions (e.g. "arms race"), but there is a recent trend towards more use of plural ones, especially in UK English. Many of these can also be and/or were originally interpreted and spelled as plural possessives....

Car sale and rule extraction are both traditionally correct. Rules extraction fits the recent trend, but cars sale would be problematic: cars' sale (the selling of cars) doesn't mean the same thing as car sale (a discount on cars).

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Car Sales seems the more correct term, unless speaking of the sale of a particular car. Cars sale seems more like a typo than anything else.

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