# Permutation Calculator Calculate permutations (nPr) and combinations (nCr) instantly with step-by-step work. Perfect for seating arrangements, passwords, and lottery odds. --- - **Canonical URL:** https://dothecalculation.com/calculators/permutation-calculator - **Category:** Math calculators - **Publisher:** Do The Calculation (https://dothecalculation.com) - **Cost:** Free, no account or sign-up required - **Privacy:** Runs entirely in the browser; inputs are never sent to a server - **Methodology:** https://dothecalculation.com/methodology --- ## Frequently asked questions ### What is a permutation calculator? A permutation calculator finds the number of ways to arrange r items from n distinct items where order matters. ### What is the permutation formula? The permutation formula is nPr = n! / (n-r)!. ### What is the difference between permutation and combination? In permutations, order matters (arrangements). In combinations, order doesn't matter (selections). ### When do I use permutations? Use permutations when the order of items matters, such as seating arrangements, passwords, or rankings. ### When do I use combinations? Use combinations when the order of items doesn't matter, such as lottery numbers, choosing a team, or picking flavors. ### What is nPr? nPr is the notation for permutations. It means the number of ways to arrange r items from n distinct items. ### What is the relationship between permutations and combinations? nCr = nPr / r!. Combinations are smaller because order doesn't matter. ### How do I compute permutations? To compute permutations: identify n and r, use the formula nPr = n!/(n-r)!, and calculate. ### What is 0!? 0! = 1 (mathematical convention). ### Can I use permutations with repetition? The standard permutation formula (nPr) is for arrangements without repetition. This calculator also supports repetition — toggle "Allow repetition" and it switches to the n^r formula automatically. ### What is the difference between nPr and nCr? nPr (permutations) is for arrangements where order matters. nCr (combinations) is for selections where order doesn't matter. ### How many ways can I arrange 5 books on a shelf? 5P5 = 5! = 5 × 4 × 3 × 2 × 1 = 120 ways. ### How many ways to choose 3 toppings from 10? 10C3 = (10 × 9 × 8) / (3 × 2 × 1) = 120 ways. ### What is a possible combinations calculator? A possible combinations calculator calculates the number of ways to choose r items from n items where order doesn't matter (combinations). ### Is this permutation calculator free? Yes — completely free with no registration required. ## Related guides - [Standard Deviation Guide: Measure Data Spread Clearly](https://dothecalculation.com/blog/math/standard-deviation-explained) — Understand variance, population vs sample formulas, and data spread with worked examples tied to the live DTC standard deviation calculator. - [Random Number Generation Guide: Seeded PRNGs, True Randomness, and Safe Use Cases](https://dothecalculation.com/blog/math/random-number-generation) — Learn the difference between deterministic seeded generators, browser pseudo-random functions, and cryptographically strong randomness so you can use the right tool for the job. ## Related calculators - [Combination Calculator](https://dothecalculation.com/calculators/combination-calculator) — Calculate combinations (nCr) instantly with step-by-step work, with or without repetition. Perfect for lottery odds, poker hands, and team selection. - [Average Calculator](https://dothecalculation.com/calculators/average-calculator) — Use our free average calculator to find the mean, weighted average, and GPA. Shows step-by-step work for any set of numbers. - [Binomial Distribution Probability Calculator](https://dothecalculation.com/calculators/binomial-distribution-calculator) — Compute binomial probability mass function, cumulative distribution, mean, and variance instantly with this free statistics calculator. - [Chi-Square Test Calculator](https://dothecalculation.com/calculators/chi-square-test-calculator) — Run a Chi-Square goodness-of-fit test on observed vs. expected category counts and get the test statistic, degrees of freedom, and p-value. - [Confidence Interval Calculator](https://dothecalculation.com/calculators/confidence-interval-calculator) — Calculate confidence intervals for population means and proportions, including margin of error, with this free statistics calculator. - [Descriptive Statistics & Outlier Detector](https://dothecalculation.com/calculators/descriptive-statistics-calculator) — Calculate variance, standard deviation, quartiles, IQR, and detect statistical outliers with box plots using this free tool. --- _Source: [Do The Calculation](https://dothecalculation.com/calculators/permutation-calculator). Quote freely with attribution and a link to this page._