Solution

The correct answer is \(\frac{1}{2}\)mn(m + n - 2)

EXPLANATION:

Let's consider a triangle with vertices B, C, and a point D on line AB. This way, we have two vertices from line AB (B and D) and one from line AC (C).

So, the vertices of the triangle would be B, C, and D.

This creates a triangle without using vertex A. If you have any specific requirements or constraints

= ^mC₂ x ⁿC₁ + ⁿC₂ x ^mC₁
\(=\frac{m(m-1)}{2} \times n + \frac{n(n-1)}{2} \times m\)
\(=\frac{mn}{2}(m - 1 + n - 1) \)
\(=\frac{mn}{2}(m + n - 2) \)