1. The faces of two identical regular tetrahedra are colored red, white, green, and blue; the colors are chosen randomly, but the four faces of each tetrahedron must all be of different colors. What is the probability that after coloring, the two tetrahedra are indistinguishable?
(A) $\frac{1}{4!}$
(B) $\frac{2}{4!}$
(C) $\frac{1}{4}$
(D) $\frac{1}{2}$
(E) 1
1. The answer is (D). We place both tetrahedra on the red face and rotate them until we have the white face in front of us. At this point, there are two possible cases, the one on the right can be green or blue. Regardless of the color of the first tetrahedron, the probability that the second one is of the same color and that the two tetrahedra are indistinguishable is $1 / 2$.