Try this problem from I.S.I. B.Stat Entrance Objective Problem based on number of triangles in a Polygon.

Number of triangles in Polygons ( B.Stat Objective Question )


For a regular polygon with n sides (n>5) the number of triangles whose vertices are joining non adjacent vertices of the polygon is

  • \({n \choose 3}\)
  • \(\frac{n(n-4)(n-5)}{6}\)
  • 0
  • none of these

Key Concepts


Polygons

Triangles

Combinations

Check the Answer


But try the problem first…

Answer: \(\frac{n(n-4)(n-5)}{6}\).

Source
Suggested Reading

B.Stat Objective Problem 105

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints


First hint

here total triangles \({n \choose 3}\)

Second Hint

\({n \choose 3}\) -n(n-4) for one side common triangles -n for two side common triangles

Final Step

=\({n \choose 3}\)-n(n-4)-n=\(\frac{n(n-4)(n-5)}{6}\).

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