Prove Sylvester Gallai Theorem using combinatorics

I have come across a question in my book which goes as follows:

Consider a finite set $S$ of points in a euclidiean plane such that not all of them are collinear. Prove that there exists a line which passes through exactly two points of $S$.

Now this result, known as Sylvester Gallai Theorem (not exactly), can be proven by me using induction but the book demands the proof using combinatorics. In this attempt for same question, the proof seems to be rather complicated.

Please help me. (Also please limit to only high school level math)

Thanks