Combinatorics Calculator

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
• nP_k = n·(n−1)·…·(n−k+1)
• nC_k = n! / (k!(n−k)!)
• With repetition: permutations = n^k; combinations = C(n+k−1, k)
• Multiset: n! / (a! b! …)
• Binomial: P(X=k) = C(n,k) p^k(1−p)^n−k

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