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Compute nCr (combinations) and nPr (permutations) with exact integer arithmetic. Supports large n via logarithms.
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Computes combinations (nCr, binomial coefficient) and permutations (nPr) with exact integer arithmetic. Supports large n via log-factorial approximation. Also shows n! for reference.
Combinatorics is essential in probability, statistics, computer science, and game theory. Exact integer arithmetic avoids floating-point overflow for moderate n, while log-factorial handles larger values.
This tool is part of the DevStackIO platform — a collection of free online developer tools from DevStackIO. Browse more free developer resources on DevStackIO.
Students, statisticians, data scientists, software engineers, lottery players, and anyone solving counting problems.
Enter n (total items) and r (items to choose/arrange)
The tool shows combinations (order doesn't matter) and permutations (order matters)
For n > 170, results use log-factorial approximation (displayed in scientific notation)
10, 352, 520, 2What's the difference between combinations and permutations?
Combinations ignore order (committee); permutations count order (ranking).
Why does n > 170 use approximation?
JavaScript's Number type overflows beyond 170! (≈7.3×10^306).
Can I calculate multinomial coefficients?
This tool handles binomial (2 categories). For multinomial, use the formula n!/(n1! n2! ... nk!).
Authoritative specifications, standards, and in-depth reading for Combinations & Permutations Calculator.
Combinations (nCr)
120
Order does not matter
Permutations (nPr)
720
Order matters
n!
3,628,800
nCr = n! / (r! × (n−r)!), nPr = n! / (n−r)!. Large values use log-factorial approximation. Runs locally.
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