How to use it
- Enter your items, separated by commas, spaces or new lines.
- Leave the length empty for all items, or enter k.
- Choose repetition and how identical items are treated.
- Read the count and copy or download the list.
Permutations in one minute
A permutation is an arrangement where order matters: ABC, ACB, BAC, BCA, CAB and CBA are six different permutations of A, B, C.
| Situation | Formula | Example |
|---|---|---|
| All n items in order | n! | 4 items: 4! = 24 |
| k of n items in order (nPr) | n! / (n − k)! | 2 of 4: 4! / 2! = 12 |
| With repetition | nᵏ | 3 positions from 4 items: 4³ = 64 |
| Items that repeat | n! / (a! · b! · …) | letters of BOOK: 4! / 2! = 12 |
The tool picks the right formula for your settings and shows it with your numbers under the result. If order doesn't matter, you need the combination generator.
Settings
- Items. Separate them with commas, spaces or new lines, or treat each character as an item (handy for words: BOOK).
- Length (k). Leave it empty to arrange all items, or enter a smaller number for partial arrangements, like the gold, silver and bronze places among 8 runners: 8 × 7 × 6 = 336.
- With repetition. Each position can use any item again, as in a 4-digit PIN from 10 digits: 10⁴ = 10,000.
- Treat identical items as the same. When your list contains the same item twice, such as the two O's in BOOK, swapping them doesn't create a new arrangement, so only distinct arrangements are listed. Turn it off to treat each copy as a separate item.
Output items are joined with a comma, space, nothing, hyphen, pipe or tab, one arrangement per line, optionally numbered.
Worked example
How many ways can you seat 3 of your 5 friends in the front row of a car? Order matters (who sits where), and no one can sit in two seats:
5P3 = 5! / (5 − 3)! = 120 / 2 = 60
Enter five names, set the length to 3, leave repetition off, and the tool lists all 60 seatings, starting Ann, Ben, Cal and Ann, Ben, Dee. If the same question allowed repeats (like a 3-letter code from 5 letters), it would be 5³ = 125.
Why the list is limited
Permutations grow very fast:
| n | n! |
|---|---|
| 5 | 120 |
| 8 | 40,320 |
| 10 | 3,628,800 |
| 13 | 6,227,020,800 |
| 20 | 2,432,902,008,176,640,000 |
The exact count is always calculated, no matter how big. The list shows at most 40,320 arrangements, which is every ordering of 8 items. Beyond that, the first 40,320 are shown. Everything runs in your browser.
Uses
- Anagrams and word games: all orderings of the letters in a short word (use “each character is an item”).
- Scheduling: every possible order of 5 presentations or tasks.
- Rankings: how many ways the top 3 can be filled from 10 contestants (720).
- Codes and passwords: counting arrangements to understand why length matters; see the password generator for real passwords.
- Testing: every order of steps or inputs.
- Math homework: check n!, nPr and multiset answers, and see the actual arrangements.
To shuffle a list into one random order instead of listing all of them, use sort lines with random shuffle.
Frequently asked questions
What is the formula for permutations?
All n items: n!. Choosing k of n in order: n! / (n − k)!. With repetition: nᵏ.
How many ways can 5 items be arranged?
5! = 120.
How do I count arrangements of a word with repeated letters?
Divide n! by the factorial of each repeat count. BOOK: 4! / 2! = 12. Enter the word, choose “each character is an item” and keep identical items treated as the same.
What is the difference between nPr and nCr?
nPr counts ordered arrangements, nCr counts unordered selections. nPr = nCr × k!.
How many permutations can it list?
Up to 40,320 (all orderings of 8 items). The exact total is always shown.
Last updated: November 12, 2026