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This might be a stupd inquiry, but I was working on something and stumbled upon this question: if say we are given $n$ points in plane that determine $k$ distinct lines, what is the number of triplets of collinear points?

Any help would be really appreciated

Sorry if it turns out to be too trivial or too hard to find some bounds. (I'm just tired of thinking about it without luck)


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up vote 1 down vote accepted

there can be many values of triplets of collinear points (3 points lying in a line) ,

minimum value can be zero if no 3 points lie in a line, in this case k = (n)C(2)

finding maximum value, if 3 points are not collinear then they form 3 lines, if 3 points become collinear then they constitute 1 line,

so every triplet of collinear points reduces the number of lines by 2,

number of triplets (maximum) = (nC2 - k)/2

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