There are unrestricted placements, since one colour has occupancy vectors. For any specified empty box, the two remaining boxes admit placements. For any specified pair of empty boxes, the one remaining box admits one placement. All three boxes cannot be empty.
The inclusion-exclusion principle therefore gives
(1)
The empty-box events are not disjoint events, so subtracting their counts without restoring their pairwise overlaps would be incorrect.

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