Permutations & Combinations Calculator
Count the ways to arrange or choose r items from n — permutations and combinations, with or without repetition, worked out exactly however big the answer.
About this tool
Use permutations when the order matters (a race podium, a PIN, a seating plan) and combinations when it doesn't (a lottery line, a hand of cards, a committee). Then decide whether the same item can be picked more than once: digits in a PIN can repeat, but a lottery ball can't come out twice. A 4-digit PIN from 0–9 has 10⁴ = 10,000 possibilities, while choosing 6 lottery numbers from 59 gives 45,057,474 combinations.
All four answers are worked out exactly using whole-number arithmetic, so even very large results are correct to the last digit. Answers longer than 21 digits are shown in scientific notation with the number of digits underneath; n and r can each go up to 5,000.