Combinatorics
Definition of Permutation
Full Permutations
Partial Permutations
The Formula P(n,k)
Relationship to Factorials
Definition and Examples
Multinomial Coefficients
Multinomial Formula
Applications to Word Arrangements
Definition and Properties
Linear vs. Circular Arrangements
Formula for Circular Permutations
Rotational Symmetry
Necklace Problems
Definition and Motivation
Basic Examples
The Subfactorial Notation
Recurrence Relation for Derangements
Inclusion-Exclusion Formula
Asymptotic Behavior
Applications of Derangements
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2. Fundamental Counting Principles
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4. Combinations