Try this problem from I.S.I. B.Stat Entrance Objective Problem based on number of triangles in a Polygon.
For a regular polygon with n sides (n>5) the number of triangles whose vertices are joining non adjacent vertices of the polygon is
Polygons
Triangles
Combinations
Answer: \(\frac{n(n-4)(n-5)}{6}\).
B.Stat Objective Problem 105
Challenges and Thrills of Pre-College Mathematics by University Press
here total triangles \({n \choose 3}\)
\({n \choose 3}\) -n(n-4) for one side common triangles -n for two side common triangles
=\({n \choose 3}\)-n(n-4)-n=\(\frac{n(n-4)(n-5)}{6}\).
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