Example Data Table
| Input words |
Length |
Unique full arrangements |
Unique selected arrangements |
Note |
| red blue green |
3 |
6 |
6 |
All words are different. |
| cat cat dog |
3 |
3 |
3 |
Two repeated words reduce total arrangements. |
| fast slow bright dull |
2 |
24 |
12 |
Only two positions are selected. |
| yes no yes maybe |
2 |
12 |
7 |
Repeated terms affect selected results. |
Formula Used
For full arrangements with all words treated as different, the formula is n!. Here, n is the total number of word positions.
For repeated words, the unique full arrangement count is n! divided by each repeated word factorial. The formula is n! / (a! × b! × c!). The values a, b, and c are repeated counts.
For ordered selections of r words without replacement, the distinct slot formula is n! / (n - r)!. The calculator also computes unique selected arrangements from repeated words using a multiset counting method.
For replacement choices, the formula is u^r. Here, u is the number of unique word types, and r is the selected length.
How to Use This Calculator
- Enter words in the text area.
- Choose how your words are separated.
- Enter an arrangement length, or leave it blank.
- Select case, punctuation, sorting, and output settings.
- Enable samples when you want a preview list.
- Press Calculate to view results below the header.
- Use CSV or PDF buttons to save your result.
Understanding Word Permutations
A word permutation is an ordered arrangement of given words. Order matters. The phrase red blue green has six full arrangements. The same three words can appear in many sequences. This calculator helps you measure those sequences without manual factorial work.
Why Repeated Words Matter
Repeated words change the answer. If a word appears twice, two swapped copies do not create a new readable arrangement. For example, cat cat dog has three unique full arrangements, not six. The calculator counts each repeated term and divides the full factorial result by the repeated factorial parts.
Useful Planning Features
You can choose an arrangement length. This is helpful when you only need two word slots from a longer list. You can also compare distinct slot arrangements, unique arrangements, and replacement choices. These views support writing prompts, puzzle design, classroom tasks, naming tests, and keyword ordering.
Clean Input Handling
Text often arrives with extra spaces, commas, or punctuation. The form lets you choose how words are separated. It can keep case, convert to lower case, or convert to upper case. It can also remove punctuation before counting. These options make the result easier to match your real task.
Sample Arrangement Preview
Large word sets can create huge totals. Generating every result may be slow or impossible to read. The preview limit keeps the page useful. It shows a controlled group of sample arrangements while still giving exact counts for the main formulas when the input size is practical.
Exporting Your Work
CSV export is useful for spreadsheet review. PDF export is useful for quick sharing, printing, or saving. Both downloads include the main input summary and calculated values. This makes the calculator suitable for lessons, reports, and reusable examples.
Best Practice
Start with clean words. Decide if repeated words should be treated as identical. Then pick the number of positions. Use full length for complete sentence rearrangement. Use a smaller length for partial lists or ordered selections. Check the sample preview before exporting results. This process gives a clear count and a practical record.
When totals grow beyond preview limits, trust the count table first. Exact totals remain visible for review. It also prevents long screens while preserving useful samples.
FAQs
What is a word permutation?
A word permutation is an ordered arrangement of words. Changing the order creates a different arrangement when the words are distinct.
How are repeated words handled?
Repeated words are counted as identical terms for unique arrangement totals. The calculator divides by repeated factorial groups.
Can I calculate only part of a word list?
Yes. Enter the arrangement length. The tool calculates ordered selections for that number of positions.
What does replacement count mean?
Replacement count allows the same unique word type to be used again in another position. It uses u raised to r.
Why is my unique total smaller than n factorial?
Repeated words reduce unique readable arrangements. Swapping two identical words does not create a new visible order.
Can this generate every permutation?
It generates a limited preview only. Large lists can create enormous outputs, so exact totals are shown instead.
What should I enter for a sentence?
Enter the sentence normally. Use auto separator for spaces, or choose punctuation removal for cleaner word counting.
What is exported in the files?
The downloads include input counts, main formulas, summary values, word frequency, and any generated sample arrangements.