Warehouse Load Balancing Triplets

Count how many distinct triplets of crate weights add up to a target load.

A loading dock has a list of crate weights waiting to be grouped into three-crate pallets, and a target pallet weight. Consider every way of choosing three different positions in the list, regardless of order. A group matches whenever the three weights at those positions add up to exactly the target. Return the total number of matching groups. Two matching groups that select the exact same three weight values only count as one - report the number of distinct weight-value combinations that match, not the number of different positions that could produce them.