Permutation Calculator
Calculate nPr permutations for ordered item selections.
GCD & LCM Calculator
About Permutation Calculator
The Permutation Calculator ($nPr$) computes the total number of ordered arrangements of $r$ elements chosen from a set of $n$ distinct elements with and without repetition, displaying factorials and full mathematical formulas.
How to Use Permutation Calculator
Step 1
Enter total items ($n$) and items to choose/arrange ($r$).
Step 2
Select whether repetition is allowed or if order is linear/circular.
Step 3
Review the step-by-step factorial cancellation formula.
Step 4
Click "Copy Result".
Practical Use Cases for Permutation Calculator
Password & PIN Security Permutation Analysis
Calculate the total number of possible ordered arrangements for 4-digit PINs ($10^4 = 10,000$) vs 8-character alphanumeric passwords ($62^8$).
Sports Tournament & Race Podium Placements
Find how many ways 1st, 2nd, and 3rd place trophies can be awarded among 12 competing athletes ($_{12}P_3 = 1,320$).
Input & Output Examples
Arranging 3 Winners from 10 Contestants
Total elements (n): 10, Chosen items (r): 3
$_{10}P_3 = \\frac{10!}{(10-3)!} = \\frac{3628800}{5040} = 720$ possible podium ordersKey Features & Performance
- ✓Calculates $nPr = \\frac{n!}{(n-r)!}$ (Without Repetition) and $n^r$ (With Repetition).
- ✓Supports Circular Permutations ($(n-1)!$) and Permutations with Indistinguishable Items ($\\frac{n!}{n_1! n_2!...}$).
- ✓BigInt arbitrary precision handles huge factorials without overflow.
- ✓100% Client-Side calculation.
- ✓1-Click Copy permutation solution.
Key Terminology & Definitions
Permutation ($nPr$)
An arrangement of objects in a specific, definite order (where the order of selection matters: $(A, B) \\neq (B, A)$).
Factorial ($n!$)
The product of all positive integers less than or equal to $n$ ($n! = n \\times (n-1) \\times \\dots \\times 1$, with $0! = 1$).