Combinations and permutations
How many ways to choose k items from n, with or without order or repetition.
How it works
Combinations C(n, k) = n! / (k!(n − k)!). Permutations P(n, k) = n! / (n − k)!. With repetition: C(n + k − 1, k) and nᵏ.
Results are for guidance only and do not replace professional advice.
Worked example
With the default values:
- n (total items)49
- k (items chosen)6
you get:
- Combinations C(n, k) (order doesn't matter)13,983,816
- Permutations P(n, k) (order matters)10,068,347,520
- Combinations with repetition25,827,165
- Permutations with repetition (nᵏ)13,841,287,201
Frequently asked questions
How does the “Combinations and permutations” tool work?
Combinations C(n, k) = n! / (k!(n − k)!). Permutations P(n, k) = n! / (n − k)!. With repetition: C(n + k − 1, k) and nᵏ.
What do I need to enter?
Just fill in: n, k. The result updates as you type.
Can you give an example?
n (total items): 49; k (items chosen): 6 → Combinations C(n, k) (order doesn't matter): 13,983,816; Permutations P(n, k) (order matters): 10,068,347,520.
Is this calculator free, and is my data private?
Yes. HOD Calc is completely free with no sign-up. The calculation runs in your browser: nothing you type is sent or stored.