The last picture is the most telling. The number of arrangements of n objects is n ! . So the number of possible arrangements of q pebbles and N ′ ′ − − 1 partitions is ( q + N ′ ′ − − 1 ) ! . However, if partition #3 and partition #5 trade places, no one would notice. The same argument goes for quanta. To obtain the number of possible distinguishable arrangements one has to divide the total number of arrangements by the number of indistinguishable arrangements. There are q ! identical quanta arrangements, and ( N ′ ′ − − 1 ) ! identical partition arrangements. Therefore, multiplicity of the system is given by