Given a convex $ n $-gon ($ n \geq 5 $). Prove that the number of triangles of area $1$ with vertices at the vertices of the $ n $-gon does not exceed $ \frac{1}{3} n (2n-5) $.
Since $\binom{n}{3}-\frac{1}{3} n (2n-5)=\dfrac{n(n-3)(n-4}{3}$ which is the number of triangles taken by selecting a vertex and then selecting a point other than its 2 neighbours and then another point other than these point but since we do this for each vertex thus we have to divide the result by tthree if only someone could interprete this for me