Well, the guitar has a finite number of strings and each string is partition into a finite number of frets. It's definitely not more than, say, 30^6 ~ 729 million.

That said, common chords are A, B, C, D, E, F, G (and their sharps and flats), combined with either major or minor mode. Hence "C, G, F, Am, Em" is an example of what someone could play. Now, of course, if it doesn't sound exactly like a G, perhaps it's a G7? After some practice, you can even hear, by the sound of the strings, exactly which chord it is. Em, G, and D are particularly simple to recognize.