AMC 10A 2009 Problem 24

Three distinct vertices of a cube are chosen at random. What is the probability that the plane determined by these three vertices contains points inside the cube?

Answer Choices
A. \dfrac{1}{4}
B. \dfrac{3}{8}
C. \dfrac{4}{7}
D. \dfrac{5}{7}
E. \dfrac{3}{4}