Interior crossings of a decagon's diagonals

In a convex decagon (10-gon) in general position, draw all the diagonals. Assuming no three diagonals meet at a single interior point, how many interior intersection points do the diagonals create?

Show hints (2)+
  1. Each interior crossing comes from a unique set of 4 vertices (a quadrilateral's two diagonals).
  2. So the count is (104)\binom{10}{4}.

Answer

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210

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