Compute factorials, permutations (nPr), combinations (nCr), multinomial coefficients, and Stirling numbers with arbitrary-precision BigInt arithmetic — handles inputs up to n = 10,000.
n! = n × (n−1) × … × 1. nPr = n! / (n−r)! counts ordered r-tuples from n items. nCr = n! / (r!(n−r)!) counts unordered subsets. Multiset C(n+r−1, r) counts unordered selections with repetition. Multinomial = n! / (k₁! · k₂! · …) counts distinct arrangements where k₁+k₂+…=n. Stirling S(n,k) counts partitions of n items into k non-empty subsets. Catalan Cₙ = C(2n,n)/(n+1) counts balanced parentheses, binary trees, and many more structures.