Triangle-Ception, Don't Lose Your Count!

Discrete Mathematics Level pending

Calvin was given 2016 line segments with lengths of \(1, 2, 3, 4,\ldots , 2015, 2016\) respectively and he had to pick three random lines to form a triangle. Determine the possible number of triangles Calvin could form.

Details and assumptions

\(\bullet\) All the lengths are in the same system of units.

This problem is inspired by a much simpler problem taken from a middle school textbook.

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