Number of Triangles in a Regular Polygon: Is nC3 the Correct Formula?

[utkarshakash]

Homework Statement

Find number of triangles which can be obtained by vertices of a regular polygon of n sides.

The Attempt at a Solution

I think it should be nC3 as forming a triangle requires you to select any 3 vertices from n available vertices. But I'm not sure whether this is correct or not. Can anyone verify it?

 

[Simon Bridge]

I think the way you would go about verifying something like that would be to draw a bunch of regular polygons, then work out the triangles - count them, and see if it agrees with nC3.
You'll at least gain confidence with each one that works - but the trick is to see if you can figure out how to get one that won't.

 

[haruspex]

You just have to satisfy yourself in regard to four questions:
1. For any such triangle, is there a selection of three vertices that produces it?
2. Does every such selection produce a triangle?
3. Does every such selection produce only one triangle?
4. For any two such selections, do they produce different triangles?