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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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