When should I use Exact versus Approx?

Exact mode uses BigInt for full-precision results up to roughly n = 10,000. If the magnitude exceeds that limit, switch to Approx to see a scientific-notation estimate and digit count instantly.

Permutation & Combination Calculator (nPr, nCr)

Q: What is the difference between permutations and combinations?

Permutations (nPr) count arrangements where order matters, while combinations (nCr) count selections where order does not. For three people choosing two, AB and BA are distinct permutations but the same combination.

Results

Exact value: —

Digits: —

Scientific notation: —

Step log

Steps are hidden. Turn on “Show steps” to view them.

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.

Related calculators

Pascal's triangle & binomial expansion (with steps)