Problem #PRU-60383

Problems Combinatorics Systems of points and line segments Systems of points and line segments (other)

Problem

On two parallel lines $a$ and $b$ , the points $A_{1}, A_{2}, \dots, A_{m}$ and $B_{1}, B_{2}, \dots, B_{n}$ are chosen, respectively, and all of the segments of the form $A_{i} B_{j}$ , where $1 \leq i \leq m$ , $1 \leq j \leq n$ . How many intersection points will there be if it is known that no three of these segments intersect at one point?

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