Ehrenfest chain. This chain originated in physics as a model for two cubical volumes of air connected by a small hole. In the mathematical version, we have two "urns," i.e., two of the exalted trash cans of probability theory, in which there are a total of N balls. We pick one of the N balls at random and move it to the other urn. Let Xn be the number of balls in the "left" urn after the nth draw. Show that Xn is a Markov process and find its one-step transition probability matrix.