Permutation & Combination Calculator
Permutations, Arrangements & Combinations C_n^k
Choose an operation, then enter n and k. The solution states the formula, substitutes the numbers, and cancels the common factorials. Permutations only need n.
The calculator above computes permutations Pₙ, arrangements Aₙᵏ, and combinations Cₙᵏ and shows the factorial formula behind each result.
Formulas used
Pₙ = n!
Aₙᵏ = n!/(n − k)!, Cₙᵏ = n!/(k!(n − k)!)
- Use arrangements when order matters and combinations when it does not.
Worked example
Choose 3 students from 10:
C(10, 3) = 120
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Enter n and k (0 ≤ k ≤ n).
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.