# Side by Side

Please throw some light on counting k-sided polygon in an n-sided polygon under different conditions viz how many triangles can be drawn using vertices of a 15 sided polygon if none of the sides of the polygon is also side of the triangle and in similar way how to find out number of hexagons,equilateral triangles,isosceles triangles etc.

Note by Galen Buhain
3 years ago

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The answer is $$\displaystyle\frac{n}{k} {{n-k-1}\choose{k-1}}$$.Hint:Stars and bars logic is involved.

- 3 years ago