Triangles across two lines

Four points lie on one straight line and three more points lie on a second, parallel line (seven points in all; no other three are collinear). How many triangles have all three vertices among these points?

Show hints (2)+
  1. Count all triples of points, then subtract the collinear ones (they aren't triangles).
  2. (73)(43)(33)\binom{7}{3} - \binom{4}{3} - \binom{3}{3}.

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30

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

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