A probability problem by Paola Ramírez

First, select the points of the base for this we will look at one horizontal line of points. The two points of the base have to have an odd number of points between them, so the points of the base have to have the same parity. we can selected of $\binom{5}{2}$ (for even points) $+\binom{6}{1}$ (for odd point), this is equal to $25$ ways of select the base of one line. Then each base could have $10$ heights(this is the third point of the triangle). Last, this happens to each pink, there is $20$ pink line $\Rightarrow$ we get $25\times10\times22=5500$