nCr & nPr calculator (permutations & combinations)

Results

Exact value: —

Digits: —

Scientific notation: —

Step log

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Teacher notes

Combination: nCr = n! / (r!(n-r)!). Symmetry C(n, r) = C(n, n-r) lets you halve the work by using k = min(r, n-r).
Permutation: nPr = n! / (n-r)!. Remember P(n, 0) = 1 and P(n, n) = n! for boundary checks.
Factorial: n! = 1 × 2 × … × n with 0! = 1. Reinforce the base case when reviewing recurrence proofs.
When inputs blow past the Exact limit (roughly n = 10,000), switch to Approx so learners still see the order of magnitude and digit count.
This tool is for educational use only. Always double-check final answers before grading or publishing materials.

FAQ

What is the difference between permutations and combinations?

Permutations treat the order of selection as unique (AB ≠ BA). Combinations treat those as the same outcome, counting only distinct subsets.

When should I switch between Exact and Approx?

Use Exact for values within the BigInt range (up to about n = 10,000 with k ≤ 5,000). Switch to Approx when the exact integer would be too large; you will still see the digit count and an accurate scientific notation.

How it’s calculated

Uses factorial identities: nCr = n!/(r!(n−r)!) and nPr = n!/(n−r)! with big‑integer safeguards.
Out‑of‑range inputs are rejected; results are formatted with grouping for readability.
The shareable URL stores n and r so you can rerun the same case.

Results

Step log

FAQ

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How it’s calculated