Combination & Permutation Calculator
Calculate nCr combinations and nPr permutations.
About this tool
Combinations (nCr) count how many ways to choose r items from n when order doesn't matter — like picking a 5-card hand. Permutations (nPr) count arrangements where order does matter — like ranking the top 3 finishers in a race. This calculates both at once from the same n and r.
Key Features
- Combinations (nCr) — order doesn't matter
- Permutations (nPr) — order matters
- Numerically stable for large n (no factorial overflow)
How to Use
- Enter n, the total number of items.
- Enter r, how many are chosen.
- Click Calculate.
Benefits
- Solve card, lottery and dice combinatorics problems
- Check probability and statistics homework
- Understand the difference between choosing and arranging
Frequently Asked Questions
nCr counts selections where order is irrelevant (a hand of 3 cards is the same hand no matter what order you were dealt them). nPr counts arrangements where order matters (1st, 2nd, 3rd place are different outcomes even with the same 3 people). nPr is always ≥ nCr for the same n and r.
Factorials grow enormously fast — 70! already exceeds what a standard number can represent precisely. This calculator multiplies and divides incrementally instead of computing full factorials, so it stays accurate for much larger values of n.