For any number of such containers their are a set number of paterns in which they can be arranged. For example five containers may be arranged in a maximum of twenty such patterns.

These "Container Numbers" are related to Rooted Trees (Graph Theory).

Related:
http://sci.tech-archive.net/Archive/sci.math/2006-10/msg07283.html http://www.combinatorics.org/Surveys/ds5/VennSeparatingEJC.html

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