47. M balls are initially distributed among m urns. At each stage one of the balls is selected at random, taken from whichever urn it is in, and then placed, at random, in one of the other M - 1 urns. Consider the Markov chain whose state at any time is the vector (ni9 ...9nm) where nt denotes the number of balls in urn /. Guess at the limiting probabilities for this Markov chain and then verify your guess and show at the same time that the Markov chain is time reversible.