Permutation Calculator
Compute permutations (nPr)—the number of ways to arrange or sequence an ordered subset of r items chosen from a distinct set of n items without replacement.
Total distinct items available to choose from
Number of items placed into ordered slots
Total possible ordered sequences or arrangements
How to Use This Calculator
- Enter the total pool of distinct items (n).
- Enter the number of items to select and order (r).
- View the total ordered arrangements and contrast with unordered combinations.
Formula & Calculation Methodology
Permutations count distinct arrangements where sequence matters. The first position has n choices, the second has n-1, continuing down for r slots.
Worked Example
Podium finishes (1st, 2nd, 3rd) from 8 racers
Arranging 4 books on a shelf from 6 available
Frequently Asked Questions
Does order matter in permutations?↓
Yes, absolutely. In permutations, AB is distinct from BA. If order does not matter, use combinations instead.
What occurs if r is greater than n?↓
It is impossible to pick more distinct items than exist in the pool without replacement, so nPr returns 0.
What is 0! (zero factorial)?↓
By mathematical definition and empty set combinatorics, 0! equals 1.
What is a limitation of permutations without replacement?↓
This calculation assumes every chosen item is unique and cannot be picked twice (like lottery balls, not PIN codes with repeats).
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.