Permutation Calculator – Guide & Formulas
Calculate permutations (nPr) where order matters. Supports selections with and without repetition.
Quickly calculate permutations (nPr) representing the number of ways to select and order "r" items from a set of "n" unique objects. Perfect for statistics students, event planners, and safety code designers.
Key Takeaway
Use the free Permutation Calculator to calculate permutations (npr) where order matters. supports selections with and without repetition. Get instant results with step-by-step explanations.
How to Use the Permutation Calculator
- Enter the total number of items in the set (n).
- Enter the number of items to select (r).
- Toggle repetition mode if selecting items multiple times.
- Review the step-by-step formula breakdown and final arrangements count.
The Formula
Variable Definitions
- n: Total number of items in the set
- r: Number of items selected
- nPr: Number of unique ordered arrangements
Creating a 3-Digit Lock Combination
Find the number of ways to create a 3-digit passcode from the numbers 0 to 9, where digits cannot repeat.
- Step 1: Input total items n = 10.
- Step 2: Input selection size r = 3.
- Step 3: Apply formula: 10! / (10 - 3)! = 10! / 7!.
- Step 4: Compute 10 * 9 * 8 = 720 unique codes.
Frequently Asked Questions
Does order matter in permutations?
Yes, the defining characteristic of a permutation is that order does matter. Selecting AB is different from selecting BA.
What is a permutation with repetition?
When repetition is allowed, the formula simplifies to n^r, because each of the r choices has n available options.
Can r be larger than n in a simple permutation?
No. Without repetition, you cannot select more items than you have in the pool. Therefore, r must be less than or equal to n.