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What are permutations and combinations?

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Quick answer

Permutations and combinations are ways to count how many arrangements or selections are possible. Permutations count when order matters (like a race finish); combinations count when order doesn't (like choosing a pizza's toppings). Both count possible arrangements or selections. Permutations: order matters (e.g., 1st, 2nd, 3rd place).

Key things to understand

  1. Both count possible arrangements or selections.
  2. Permutations: order matters (e.g., 1st, 2nd, 3rd place).
  3. Combinations: order doesn't matter (e.g., a group of friends).
  4. They're foundational to probability and statistics.

People also ask

What's the difference between a permutation and a combination?
Permutations care about order; combinations don't. 'AB' and 'BA' are two permutations but one combination.
When do you use permutations?
When the order of selection matters — like rankings, passwords, or seating arrangements.
When do you use combinations?
When order doesn't matter — like choosing a team, lottery numbers, or pizza toppings.