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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

But try the problem first…

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

Source

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