Permutation and Combination Calculator

nPr and nCr for choosing k items from n.

Permutation and Combination Calculator helps you nPr and nCr for choosing k items from n. Enter total items (n) and items chosen (r), review the breakdown, and use the guidance below to understand what the number means — and what it does not. What the Permutation and Combination calculator does Permutation and Combination Calculator is built for arithmetic, algebra, geometry, and number tools. nPr and nCr for choosing k items from n. You enter total items (n) and items chosen (r), then Simple Calculators computes the result instantly. Results use standard school and engineering formulas that run privately in your browser. How the math works Enter Total items (n) and Items chosen (r); both are rounded to whole numbers, r cannot be more than n, and n can be at most 170. Permutations (order matters) = n! ÷ (n − r)!, and combinations (order does not matter) = n! ÷ (r! × (n − r)!), where n! (n factorial) means n × (n − 1) × … × 1. Very large answers are shown in scientific notation, and a table compares the counts for nearby values of r. The formula: Permutations = n! ÷ (n − r)!; Combinations = n! ÷ (r! × (n − r)!). Use permutations when order matters and combinations when it does not. …