There are 26 possible distributions of 9 units of energy among 6 particles, and if those particles are indistinguishable and described by Bose-Einstein statistics, all of the distributions have equal probability. To get a distribution function of the number of particles as a function of energy, the average population of each energy state must be taken. The average for each of the 9 states is shown below compared to the result obtained by Maxwell-Boltzmann statistics.
Low energy states are more probable with Bose-Einstein statistics than with the Maxwell-Boltzmann statistics. While that excess is not dramatic in this example for a small number of particles, it becomes very dramatic with large numbers and low temperatures. At very low temperatures, bosons can "condense" into the lowest energy state. The phenomenon called Bose-Einstein condensation is observed with liquid helium and is responsible for its remarkable behavior.