Counting Principles: Permutations and Combinations
By Dr. Iris Vaughan, Mathematics Editor·Published 15 November 2025·Last reviewed 25 January 2026
Multiplication principle, permutations (with and without repetition), combinations, and the Pascal's triangle connection — with worked examples.
Key Formulas
Multiplication: n₁·n₂·...·nₖ total arrangements
P(n,r)=n!/(n−r)! with order
C(n,r)=n!/(r!(n−r)!) without order
With repetition: nʳ permutations
Pascal: C(n,r)=C(n−1,r−1)+C(n−1,r)
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