On two parallel lines $a$ and $b$, points $A_{1}, A_{2}, \ldots, A_{m}$ and $B_{1}, B_{2}, \ldots, B_{n}$ are chosen respectively, and all segments of the form $A_{i} B$

$(1 \leq i \leq m, 1 \leq j \leq n)$ are drawn. How many intersection points will there be, given that no three of these segments intersect at the same point?
Every two intersecting segments are diagonals of a quadrilateral, two vertices of which lie on $a$, and the other two - on $b$.

See also problem $\underline{30695}$.

## Answer

$C_{m}^{2} C_{n}^{2}$ points.