Count selections and ordered arrangements
Enter the total number of distinct items n and the number to select r. Combinations count selections where order does not matter. Permutations count arrangements where order matters. Selecting five cards from 52 gives 2,598,960 combinations and 311,875,200 ordered arrangements.
How the formulas work
Permutations use nPr = n! / (n-r)!. Combinations use nCr = n! / (r! × (n-r)!). The calculator multiplies and divides integers exactly, so large answers do not lose digits through floating-point rounding.
Assumptions and limits
Items must be distinct and cannot be reused within a selection. Both inputs must be whole numbers from 0 to 1,000, with r no larger than n. Selecting zero items gives one empty selection and one empty arrangement, including when n is zero. This tool does not model repeated items or selections with replacement.
Local browser calculation
Calculations run in this browser tab. Your numbers are not uploaded to a server.