Two different solutions are available, the official one (considering the possible convex hulls), and an alternative one, looking at subsets of at least $3$ collinear points in $S$. Both are in fact elementary at heart, and easily point to all possible configurations (out of which only the one on $6$ points arranged in two imbricated triangles, with three sets of $3$ collinear points each, is challenging to find, and interesting per se). Not the most difficult Problem 3 ever seen in such a test ...

I don't think collinear points are accepted since it was written that "intersect in only one point " ..!! So if you got A,B,C are collinear in this order then consider AB intersect AC at segment BC which is not "only one point" Am I right ..?

No, you're wrong. The statement says: if the segments intersect in one point; in your example, segments $AB$ and $AC$ intersect over all $AB$, so this is not part of the implication.

Oh, you're right.