Smart Math guide · Statistics & Probability

Permutation or Combination?

Use permutations when order matters and combinations when order does not.

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The method

How to use it

  1. Ask whether rearranging the same chosen items creates a new outcome.
  2. Use nPr for order-sensitive selection.
  3. Use nCr for order-insensitive selection.
Worked example

See it in action

Choosing president and vice president from 5 people: 5P2=20; choosing any 2-person committee: 5C2=10.

Check your thinking

How to verify it

Ordered count should be larger here because AB and BA differ.

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