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Combinations count ways to choose items where order does not matter. Permutations count ways where order does matter. Both use factorials and appear in probability, statistics, and combinatorics.

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1. 1Permutations (order matters): P(n,r) = n! / (n−r)!
2. 2Combinations (order irrelevant): C(n,r) = n! / (r!(n−r)!)
3. 3Rule of thumb: if you can swap two items and get a different result, use permutations

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