Combination Calculator (nCr)
Enter the total number of items (n) and how many you’re choosing or arranging (r) to calculate combinations or permutations.
Combinations vs. permutations
Both count the ways to pick r items from a group of n items, but they answer different questions. A combination (written nCr) counts the ways to choose items when the order doesn’t matter, like picking a group of 3 people from 10. A permutation (written nPr) counts the ways to arrange items when order does matter, like awarding 1st, 2nd, and 3rd place among 10 runners.
How this calculator works
Combinations use the formula nCr = n! / (r! x (n-r)!), and permutations use nPr = n! / (n-r)!, where ‘!’ means factorial (the product of all positive integers up to that number). This calculator uses an equivalent step-by-step multiplication method so it stays accurate even for larger values of n, rather than computing full factorials directly.
Both n and r must be whole numbers, and r cannot be greater than n. This tool is intended for general educational purposes.