math

Permutation & Combination

Methods of counting arrangements: permutations count ordered arrangements, combinations count unordered selections.

Permutations count arrangements where order matters. Combinations count selections where order doesn't matter.

Formulas

  • Permutation: nPr = n! / (nβˆ’r)!
  • Combination: nCr = n! / [r!(nβˆ’r)!]

Example

Choosing 3 from 10 people:

  • Permutation (order matters β€” President, VP, Treasurer): 10P3 = 720
  • Combination (committee of 3 β€” order doesn't matter): 10C3 = 120

nPr is always β‰₯ nCr because permutations count more arrangements.

Related Calculators

Related Terms