Combinatorics

Permutation Combination Calculator

Evaluate permutations, combinations, and factorials using precise big-integer arithmetic—perfect for counting problems.

permutationcombinationfactorial

Permutation & Combination

Calculate nPr and nCr along with n! using exact integer arithmetic.

3628800

nPr

5040

nCr

210

Counting formulas

nPr = n! / (n − r)!
nCr = n! / (r! (n − r)!)

Big integers keep results exact even for large n (up to 300). Outputs are displayed in standard or scientific notation depending on magnitude.

Enter n (the total items) and r (items selected or arranged).
Review n!, nPr, and nCr instantly—values are exact integers.
Use the formatted result in proofs, probability setups, or combinatorics homework.

Example

Input: n = 10, r = 4

Output: 10! = 3,628,800; 10P4 = 5,040; 10C4 = 210

What if r > n?

Permutations and combinations are undefined when r exceeds n, so the calculator prompts you to adjust the inputs.

How large can n be?

Values up to n = 300 are supported. Beyond that, factorials exceed the safe range for display and may be unwieldy.