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.

#Geometry

Easy Math Editor

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Comments

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

Akshay Bodhare - 6 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$