How permutation and combination calculator works
Permutations and combinations both count the ways to choose r items from a set of n, but they differ in whether order matters. A permutation counts ordered arrangements (nPr = n! / (n−r)!) — picking a president then a vice-president. A combination counts unordered selections (nCr = n! / (r! × (n−r)!)) — picking a committee of two where roles do not matter.
Because order matters in permutations but not combinations, nPr is always greater than or equal to nCr for the same n and r. The combination formula divides the permutation formula by r!, removing the r! ways to reorder each chosen group. Both reduce to 1 when r is 0 (one way to choose nothing) and are undefined when r exceeds n.
Enter n (the total number of items) and r (how many to choose), then pick Permutation, Combination, or Both. The calculator evaluates the factorials and reports the result. It is commonly used in probability, statistics, lottery odds, and counting problems in discrete mathematics.