Objects are distinguishable when each has an identity or label, so interchanging two objects gives a different arrangement. Objects are indistinguishable when only their numbers or occupied positions matter and interchanging them does not give a new arrangement. This distinction changes the enumeration of distributions in the occupancy problem and the twelvefold way.
Distinguishable Objects
See also
Indistinguishable Objects, Occupancy Problem, Twelvefold WayExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Distinguishable Objects." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DistinguishableObjects.html