Combinations & Permutations (nCr, nPr)
Compute nPr and nCr from n and r. Permutations count ordered arrangements; combinations count unordered selections — with both formulas worked out.
About this calculator
Enter the total number of items n and the number chosen r (with r ≤ n). Permutations nPr = n!/(n−r)! count selections where order matters; combinations nCr = n!/(r!·(n−r)!) count selections where order does not matter. Values are computed exactly for moderate n; very large results are shown in scientific notation as approximations.
Combinations vs. permutations
A permutation counts how many ways you can arrange r items chosen from n when the order matters — nPr = n!/(n−r)!. A combination counts how many ways you can choose r items from n when the order does not matter — nCr = n!/(r!·(n−r)!). Because every combination of r items can be arranged in r! different orders, nPr is always exactly r! times nCr. For example, choosing 2 letters from {A, B, C}: there are 3 combinations (AB, AC, BC) but 6 permutations (AB, BA, AC, CA, BC, CB). Both calculations require r ≤ n, and either reduces to 1 when r = 0 or r = n for combinations.