Combinatorics Calculator
n!
3,628,800
Permutations of n elements (n!)
3,628,800
Permutations P(n,k) without repetition
720
Arrangements with repetition n^k
1,000
Combinations C(n,k) without repetition
120
Combinations with repetition
220
FAQ
Combinatorial math
Permutation vs combination?
In permutations order matters (ABC ≠ BCA), in combinations it does not (ABC = BCA). P(n,k) = n!/(n-k)!, C(n,k) = n!/(k!(n-k)!).
When to use arrangements with repetition?
When elements can repeat (e.g. 4-digit PIN, each digit 0-9): n^k. For 4 digits from 10 = 10⁴ = 10000.
What is the difference between permutations and combinations?
In permutations the order counts, so ABC differs from BCA, while in combinations it does not. The formulas are P(n,k) = n!/(n-k)! for permutations and C(n,k) = n!/(k!(n-k)!) for combinations.
Which values of n and k does the calculator take?
It takes k between 0 and n, with n up to 170. Past that the factorial runs beyond the numbers a computer can represent, and the page shows an error message instead of a result.
How are arrangements with repetition worked out?
Arrangements with repetition come to n raised to the k, because every item can come round more than once. For a four digit PIN from 0 to 9 that is 10 to the fourth, so 10000 combinations.