  We study a multiple-urn version of the Ehrenfest model. In this setting, we
denote the n urns by Urn 1 to Urn n, where n>=2. Initially, M balls are
randomly placed in the n urns. At each subsequent step, a ball is selected and
put into the other n-1 urns with equal probability. The expected hitting time
leading to a change of the M balls' status is computed using the method of
stopping times. As a corollary, we obtain the expected hitting time of moving
all the M balls from Urn 1 to Urn 2. This proves a conjecture which was
recently made in Chen et al.(2017).
