How many distinct triangles can be constructed by choosing three vertices from among the corners of a unit cube?

Answer 1

The cube has 8 vertices.

The number of ways to construct a triangle is (8 x 7 x 6) = 336 .

But there are 6 ways to wind up with the same triangle.

So the number of distinct ones is ( 8! )/( 5! x 3! ) = 56 .