How many triangles with same color are there using $6$ points?
How many triangles with same color are there using $n$ points?
It seems to be Ramsey numbers but in that we never prove there are two we prove there is minimum $1$ such triangle.For the second problem the book gave the answer
$$\binom{n}{3}-\frac{n*\lfloor{\frac{n-1}{2}}\rfloor*\lceil{\frac{n-1}{2}}\rceil}{2}$$
Which is colmpletly odd for me.Any hints?
Edit:We use two colors.None of three points are on one line and by same colore I mean both are blue or both are red.