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Overview

  • Counting as an idea
  • Combinatorics and the Factorial
  • Combination vs Permutation

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nPr vs nCr

FeaturenPr (Permutation)nCr (Combination)
MeaningArrangements of items where order mattersSelection of items where order does not matter
FormulaP(n,r)=n!(n−r)!P(n, r) = \frac{n!}{(n - r)!}C(n,r)=n!r!(n−r)!C(n, r) = \frac{n!}{r!(n - r)!}
Common UseCreating passwords, seating charts, or race rankings (1st, 2nd, 3rd)Choosing a committee, drafting a team, or selecting lottery numbers
RelationP(n,r)=C(n,r)×r!P(n, r) = C(n, r) \times r!C(n,r)=P(n,r)r!C(n, r) = \frac{P(n, r)}{r!}