3. Using the vertices of a cube as vertices, how many triangular pyramid can you form?
(A) 54 ;
(B) 58 ;
(C) 60 ;
(D) 64 ;
(E) 70 .
3. Answer: (B).
There are 8 vertices in a cube. Any 4 vertices form a triangular pyramid unless they lie on the same plane.
$$
\binom{8}{4}-6-6=58
$$