1. In a convex $n$-sided polygon, no three diagonals are concurrent. How many intersection points can all the diagonals produce?
1. The set of diagonal intersection points and the set of quadruples generated by the $n$ vertices of an $n$-sided polygon form a $1-1$ mapping, so the number of diagonal intersection points equals the number of quadruples generated by the $n$ vertices, i.e., $C_{n}^{4}$.