nPr and nCr for counting problems.
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Permutations (nPr) count ordered arrangements; combinations (nCr) count unordered selections. nPr = n!/(n−r)!, nCr = n!/(r!(n−r)!).
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Permutations care about order; combinations don't.
Number of ordered arrangements of r from n.
Number of unordered selections of r from n.
Very large n may exceed precision; results are exact for moderate n.