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Combinatorics Calculator

n & k
n (≥ 0)
k (0…n)
Permutations (nPk)
311875200
Permutations with repetition (n^k)
380204032
Combinations (nCk)
2598960
Combinations with repetition C(n+k-1,k)
3819816
Options
Display
Affects floating probabilities & scientific notation precision.
Exact thresholds
Above limits, switch to Stirling/Log approximations.
Modulo (optional)
Applies to integer results shown on each tab when exact BigInt is computed.

About the Combinatorics Calculator

Quickly evaluate factorials, permutations, combinations (with/without repetition), multiset permutations, and binomial probabilities. Exact integer results use BigInt within safe thresholds; beyond those, Stirling and logarithmic approximations provide digits and magnitudes without freezing your browser.

Formulas

  • n! = 1·2·…·n
  • nPk = n·(n−1)·…·(n−k+1)
  • nCk = n! / (k!(n−k)!)
  • With repetition: permutations = nk; combinations = C(n+k−1, k)
  • Multiset: n! / (a! b! …)
  • Binomial: P(X=k) = C(n,k) pk(1−p)n−k

For very large inputs, the tool reports digit counts and log10 values rather than full integers.