Permutation and combination calculator
Calculate factorial, permutations and combinations, with and without repetition, showing the formula.
Permutations and combinations.
Available in: 
Permutation and combination calculator: what it is for
The calculator shows at once the factorial, permutation, simple arrangement (nPr) and combination (nCr), plus arrangements and combinations with repetition, for the n and p you type.
It works with big numbers, like the 50,063,860 combinations of a 6-of-60 lottery.
How to use
- Type the total number of items (n).
- Type how many are chosen (p).
- See all the results and formulas.
When to use it
- Math homework and exams.
- Work out lottery odds.
- Count possible passwords and combinations.
Frequently asked questions
What is the difference between a permutation and a combination?
In a permutation the order matters (a podium: 1st, 2nd and 3rd place). In a combination the order does not matter (choosing 3 people for a committee).
How many tickets are possible in a 6-of-60 lottery?
Combinations of 60 numbers taken 6 at a time: 50,063,860 possible tickets. Type n = 60 and p = 6 to check.
Is it really free?
Yes, 100% free. No sign-up, no subscription and no usage limits. All Tools123 tools are free and run right in your browser.