Permutations & Combinations Calculator

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Select permutations or combinations based on whether order matters.

Permutations

Order matters - Arrangements where sequence is important

Combinations

Order doesn't matter - Selections where sequence is irrelevant

Permutations vs Combinations: What’s the Difference?

The fundamental difference lies in whether the order of items matters.

Permutations (Order Matters)

Imagine a combination lock (which should really be called a permutation lock!). The code 1-2-3 is different from 3-2-1.

  • Keywords: Arrange, Schedule, Order, Sequence
  • Formula: nPr=n!(n−r)!nPr = \frac{n!}{(n-r)!}

Combinations (Order Doesn’t Matter)

Imagine a fruit salad. Mixing apples, bananas, and grapes is the same as mixing grapes, bananas, and apples.

  • Keywords: Select, Choose, Group, Sample
  • Formula: nCr=n!r!(n−r)!nCr = \frac{n!}{r!(n-r)!}