Enter how many items you have (n) and how many you choose (r). Get both nCr (combinations, order doesn’t matter) and nPr (permutations, order matters) — exact whole numbers, even for large n.
Results update as you type. n and r must be whole numbers with 0 ≤ r ≤ n.
A combination counts how many ways you can choose r items from n when order does not matter. A permutation counts how many ways you can arrange r items from n when order does matter, so there are always at least as many permutations as combinations.
The number of combinations is nCr = n! ÷ (r! × (n − r)!). For example, choosing 2 from 5 gives 5! ÷ (2! × 3!) = 120 ÷ (2 × 6) = 10.
The number of permutations is nPr = n! ÷ (n − r)!. For example, arranging 2 from 5 gives 5! ÷ 3! = 120 ÷ 6 = 20.