Permutations & combinations calculator

How it works

Enter n (how many items) and r (how many you choose).

The formula

Permutations (order matters): nPr = n! ÷ (n − r)!. Combinations (order doesn't matter): nCr = n! ÷ (r! (n − r)!).

Worked example

Choosing 3 of 5: 5P3 = 120 ÷ 2 = 60 ordered arrangements; 5C3 = 120 ÷ (6 × 2) = 10 groups.

Good to know

• n! grows very fast: 20! is already about 2.4 × 10¹⁸.