Permutation & Combination Calculator
Use this free Permutation Combination Calculator to calculate your Permutations and combinations instantly and accurately.
Values
Result
What is a Permutation & Combination Calculator?
This calculator computes the number of ways to select and arrange items. It calculates both permutations (nPr, where order matters) and combinations (nCr, where order does not matter) for any given n and r.
How to calculate permutations and combinations manually (the formulas)
nPr = n! / (n − r)!. nCr = n! / (r! × (n − r)!). For example, nPr(10, 3) = 10 × 9 × 8 = 720. nCr(10, 3) = 720 / 6 = 120.
Example calculation
For 10 items choosing 3: nPr = 10 × 9 × 8 = 720 ordered arrangements. nCr = 720 / (3 × 2 × 1) = 120 unordered combinations.
Common mistakes
- Confusing nPr and nCr — Use nPr when order matters (e.g., rankings). Use nCr when it does not (e.g., lottery numbers).
- Forgetting that r cannot exceed n — You cannot choose more items than are available.
- Miscomputing factorials for large n — Factorials grow extremely fast. 20! is already 2.4 quintillion.
Frequently asked questions
What is the difference between a permutation and a combination?
Order matters in permutations, not in combinations.
What is nPr?
Number of ordered arrangements: n! / (n − r)!.
What is nCr?
Number of unordered combinations: n! / (r! × (n − r)!).
When should I use permutations vs combinations?
Permutations for sequences, combinations for groups.
What does n! (factorial) mean?
Product of all integers from 1 to n.
Can n be larger than r?
Yes, n must be ≥ r.