Counting disjoint 2-partitions for points in the plane

Disjoint partitions, and its counting, have been widely studied in the literature of optimal partitions and clustering. We give an exact counting on the number of disjoint ordered 2-partitions for n   points in general position in R2R2. We also give an exact counting on the maximum number of disjoint 2-partitions, where one part consists of two points, over all sets of n   points in R2R2.