Objects are indistinguishable when they have no individual labels, so interchanging two objects does not give a new arrangement. Treating objects as indistinguishable instead of distinguishable changes the enumeration of distributions in the occupancy problem and the twelvefold way.
Indistinguishable Objects
See also
Distinguishable Objects, Occupancy Problem, Twelvefold WayExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Indistinguishable Objects." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IndistinguishableObjects.html