After they had done so, she looked at their sets and told the class, "the union of these three sets is the first ten counting numbers, but their intersection is empty!"

How many triples (A, B, C) of sets are there such that

`A `U` B `U C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

and

`A ∩ B ∩ C = {}` ?