Permutations & Combinations
nPr and nCr for counting problems.
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The formula
nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!)
Both count how many ways you can pick r items from n. Permutations count ordered picks (gold/silver/bronze), combinations count unordered ones (a committee of three). Every combination corresponds to r! permutations, which is why nCr is always the smaller number.
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Frequently asked questions
When do I use permutations vs combinations?+
Use permutations when order matters (e.g. race finishes) and combinations when it does not (e.g. picking a committee).
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