1. Suppose five balls are distributed into three urns according to the Bose-Einstein scheme. Find the probability that at least one urn contains three or more balls.
2. Suppose five balls are distributed into three urns according to the Bose-Einstein scheme. Find the expected value of the number of empty urns.
3. Suppose five balls are distributed into three urns according to the Maxwell-Boltzmann scheme, but the probabilities that a particular ball drops into the three urns are :6; :3; :1, respectively. Find the expected value of the number of empty urns.
Hint: Try indicator variables.