Permutation and Combination Calculator
Count arrangements (nPr) and selections (nCr) instantly.
The Permutation and Combination Calculator counts the two classic selection problems: permutations (nPr — ordered arrangements) and combinations (nCr — unordered selections). Enter n and r and read the count with the formula behind it.
The distinction drives real math: the number of ways to award gold, silver and bronze to 10 racers is a permutation (10P3 = 720, because order matters), while the number of possible 6-number lottery draws from 49 is a combination (49C6 = 13,983,816, because draw order does not). Choosing the wrong one off by a factor of r!.
Results are exact integers for practical ranges, with a clear warning when a value exceeds numeric precision. Everything runs locally in your browser.
Permutations
720
10P3 = 10! ÷ (10−3)!
Permutations count ordered arrangements (podium orders); combinations count unordered selections (lottery tickets). For lottery odds, use combinations — the chance of picking 6 of 49 is 1 in 13,983,816.
How to use the Permutation and Combination Calculator
- Choose permutations (order matters) or combinations (order ignored).
- Enter n — the total number of items.
- Enter r — how many you choose.
- Read the count and the formula.
- Flip between modes to see how much ordering multiplies the options.
Frequently asked questions
What is the difference between a permutation and a combination?
Permutations count ordered arrangements — ABC, ACB, BAC are different. Combinations count unordered selections — ABC is one choice. Combinations are therefore r! times fewer than permutations of the same n and r.
How do I calculate lottery odds?
The number of possible draws is 49C6 = 13,983,816, so a single ticket has a 1 in ~14 million chance. The calculator gives the total — your odds are 1 over that number.
When do the numbers get too large?
nPr and nCr grow factorially — 100C50 is about 10²⁹. The calculator flags results beyond JavaScript's exact numeric range rather than returning a rounded guess.
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