Combinatorics · Lesson
When some elements are equal, swapping equal copies does not create a new arrangement. We therefore divide by the factorials of the multiplicities.
Prerequisites: Simple permutations and factorial
Goal: Remove duplicates caused by repeated elements using n!/(n1!n2!…).
Change the data, observe how the number of cases changes, and use the lab to understand the counting structure you are using.
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Imagine temporarily labelling the equal copies: you would have n! arrangements, but many represent the same anagram.
Data / situation: How many distinct anagrams does the sequence AABBCC have?
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.