About Permutations (nPr)
Combinatorics is the math of counting. A Permutation calculates the number of ways to arrange a subset of items, where order matters. The distinction of "order matters" is the key difference between this and Combinations.
The "Lock" Analogy
A "Combination Lock" is actually a misnomer; it should be called a "Permutation Lock". Why? Because the code 1-2-3 is different from 3-2-1. The order of numbers opens the lock. This is a Permutation.
The Formula: nPr
P(n, r) = n! / (n - r)!
Where n! is the factorial (e.g., 5! = 5*4*3*2*1).
Example
In a race with 8 horses (n=8), how many ways can we predict the Top 3 (r=3) in exact order (Win, Place, Show)?
Calculation: 8 * 7 * 6 = 336 ways.
Note: If we didn't care about order (just "who finishes top 3"), the answer would be much smaller (56).
How to Use
Enter the total number of items (n) and the number of items you are selecting (r). The result shows the total unique arrangements.