Permutation Calculator
Our Permutation Calculator helps you find the number of possible arrangements when selecting a specific number of items from a larger set, where the order of selection matters. It's perfect for students tackling probability and combinatorics problems.
Enter the total number of distinct items available.
Enter how many items you want to arrange from the total.
Our Permutation Calculator helps you find the number of possible arrangements when selecting a specific number of items from a larger set, where the order of selection matters. It's perfect for students tackling probability and combinatorics problems.
The formula for permutations is: P(n, r) = n! / (n-r)! Where: n = total number of items r = number of items to choose! = factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1)
Imagine you have 7 different books, and you want to arrange 3 of them on a shelf. How many different ways can you arrange these 3 books? Here, n = 7 (total books) and r = 3 (books to arrange). P(7, 3) = 7! / (7-3)! = 7! / 4! = (7 × 6 × 5 × 4 × 3 × 2 × 1) / (4 × 3 × 2 × 1) = 7 × 6 × 5 = 210. There are 210 different ways to arrange 3 books from a set of 7.
A permutation is an arrangement of items where the order of selection matters. For example, arranging the letters ABC, ACB, BAC, BCA, CAB, CBA are all different permutations of the same three letters.
The key difference is order. In permutations, the order of items matters (e.g., ABC is different from ACB). In combinations, the order does not matter (e.g., ABC is considered the same as ACB). Think of a padlock code (permutation) versus picking lottery numbers (combination).
Use it when you need to find the number of ways to arrange a subset of items from a larger set, and the sequence or position of the items is important. Common examples include arranging people in a line, ordering books, or creating passwords.
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