Permutation Calculator
Calculate the number of ways to arrange r items selected from a set of n distinct items, where order matters. Uses the formula P(n,r) = n! / (n−r)!.
About this Calculator
Calculate the number of ways to arrange r items selected from a set of n distinct items, where order matters. Uses the formula P(n,r) = n! / (n−r)!.
Formula & Calculations
Formula
P(n,r) = n! / (n−r)!Where:
- n=Total number of distinct items
- r=Number of items to select and arrange (0 ≤ r ≤ n)
- P(n,r)=Number of permutations (ordered arrangements)
Assumptions
- Order matters: arranging r items in a different order counts as a different permutation.
- Repetition is not allowed; all n items are distinct.
- r must be ≤ n and r, n must be non-negative integers.
Calculation Examples
Example 1
First pick has 10 options, second has 9, third has 8, fourth has 7. 10 × 9 × 8 × 7 = 5,040.
Example 2
All items arranged: 5! = 5 × 4 × 3 × 2 × 1 = 120.
Frequently Asked Questions
What is the difference between permutation and combination?
Permutation considers order (arrangement matters). Combination ignores order (selection only). For the same n and r, permutations are always greater than or equal to combinations: P(n,r) = C(n,r) × r!.
What are some real-world examples of permutations?
Arranging books on a shelf, determining race finishing orders, PIN code possibilities, seating arrangements at a table, and license plate combinations are all permutation problems.