Permutation and Combination Calculator
Count permutations (nPr, order matters) and combinations (nCr, order doesn't), with and without repetition.
Change the values and press Calculate to work out your own figures.
Enter the number of objects and how many are chosen.
Show the working
- nPr = n! ÷ (n − r)! = 6! ÷ 4! = 30
- nCr = n! ÷ (r! (n − r)!) = 15
How to use it
Enter the number of objects and how many are chosen.
Probabilities can be typed as decimals, fractions or percentages. Show the working gives the formula with your numbers in it.
Key facts
nPr = n! ÷ (n − r)!; nCr = n! ÷ (r! (n − r)!)
Order matters or not?
Choosing a president, secretary and treasurer is a permutation (who gets which job matters); choosing a committee of three is a combination.
Questions
What is 6P2 and 6C2?
30 and 15.
How many lottery combinations are there in 6 from 49?
13,983,816.
Formulas
nPr = n! ÷ (n − r)!; nCr = n! ÷ (r! (n − r)!)
Sources
Limitations
- Probabilities can be typed as decimals (0.25), fractions (1/4) or percentages (25%).