How many ways can MISSISSIPPI be rearranged? Not eleven factorial, because four I and four S repeat. This generator draws real anagrams and shows exactly how much the repeated letters cut the total by.
Arrangements of the letters in committee - the exact count
How many ways can MISSISSIPPI be rearranged? Not eleven factorial, because four I and four S repeat. This generator draws real anagrams and shows exactly how much the repeated letters cut the total by.
The letters in committee can be put in order in a fixed number of distinct ways, and it is almost always smaller than the factorial of the length. The reason is repetition: swapping two identical letters changes nothing you can see, so the count is the number of letters factorial divided by the factorial of each repeat. That division is the whole difference between the answer a textbook wants and the answer people guess. The calculator above reports the exact figure for committee, names which letters repeat, shows the divisor they produce, and draws a sample of real rearrangements so you can see what the arithmetic is counting.
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MISSISSIPPI has 34,650 arrangements, not the 39,916,800 that eleven letters suggest
Eleven letters can be ordered in 39,916,800 ways, but MISSISSIPPI is built from only four distinguishable letters: one M, four I, four S and two P. Swapping two of the four S characters changes nothing you can see. Divide by the repeats and the honest count drops to 34,650, which is 1,152 times smaller. This generator does that division for you and then draws real rearrangements from what is left.
How to generate anagrams step by step
- Word or phrase - from 2 to 20 characters. Spaces and punctuation count toward that limit even when you strip them out afterwards.
- How many anagrams - from 1 to 20. If the text has fewer arrangements than you asked for, you get all of them and the tool tells you so instead of quietly returning a short list.
- Strip spaces and punctuation - Yes turns THE CLASSROOM into THECLASSROOM and shuffles all twelve letters together, which is what you want for finding a hidden phrase. No keeps every character in play, including the space, so the space itself gets shuffled around with the letters.
- Read the arrangement count - the second output tells you how many distinct orderings exist and, when there are repeated letters, exactly how much they cut the total by.
- Run it again for a different draw - the results are sampled at random, not listed in order, so a second run on the same word gives a different ten.
Eight things people use this for
Case 1: checking whether two words are really anagrams
Situation: you suspectASTRONOMER and MOON STARER are the same letters.What to do: run both with stripping on and compare the arrangement counts.
Result: both report 907,200. Identical counts mean identical letter multisets, which is what being an anagram means.
Case 2: a crossword clue that says "anagram of"
Situation: the clue gives you seven letters and a definition.What to do: generate twenty variants and read down the list for something that fits the definition.
Result: twenty out of 5,040 for seven distinct letters. Not exhaustive, but the eye is fast at spotting a real word in a column of twenty.
Case 3: naming a character or a band
Situation: you want a name derived from your own, but not obviously so.What to do: enter the name, strip the space, take twenty draws.
Result: a ten letter name with two repeated pairs gives you 907,200 to choose from, so nobody will guess the source.
Case 4: teaching the multinomial in a math class
Situation: you need a worked example of why repeated items divide a factorial.What to do: enter LEVEL, then ELVIS, both five letters.
Result: LEVEL gives 30, ELVIS gives 120. Same length, four times the difference, because LEVEL has two L and two E.
Case 5: a puzzle where every arrangement matters
Situation: you want to see all of them, not a sample.What to do: pick a short word with repeats, such as AABB, and ask for twenty.
Result: the tool returns 5 and says so, because AABB has 6 arrangements in total and one of them is AABB itself.
Case 6: word games with a fixed rack of letters
Situation: seven tiles and no idea what they spell.What to do: type the tiles in any order and generate twenty.
Result: the generator does not know which strings are words, so treat the list as a prompt for your own recognition rather than an answer.
Case 7: obscuring a label in test data
Situation: you need placeholder strings that look like text but carry no meaning.What to do: shuffle a real label and take the output.
Result: strings with a plausible letter distribution, unlike random characters, which is what makes layouts break realistically.
Case 8: settling how big the search space really is
Situation: somebody claims a twelve letter phrase has "half a billion" anagrams.What to do: enter it and read the second output.
Result: for THE CLASSROOM it is 119,750,400, not the 479,001,600 that twelve letters alone would give, because of the two S and the two O.
Reference table: how repeated letters cut the count
The formula is the number of letters factorial, divided by the factorial of each repeat count. The Letters column counts what is left after spaces and punctuation are stripped, which is why THE CLASSROOM is listed as twelve. The last two columns are the total before and after dividing by the repeats, so the cost of the repetition is the ratio between them.
| Text | Letters | Repeats | If all were different | Actual arrangements |
|---|---|---|---|---|
| ELVIS | 5 | none | 120 | 120 |
| LEVEL | 5 | L twice, E twice | 120 | 30 |
| LISTEN | 6 | none | 720 | 720 |
| COFFEE | 6 | F twice, E twice | 720 | 180 |
| ANAGRAM | 7 | A three times | 5,040 | 840 |
| DORMITORY | 9 | O twice, R twice | 362,880 | 90,720 |
| ASTRONOMER | 10 | O twice, R twice | 3,628,800 | 907,200 |
| BOOKKEEPER | 10 | O twice, K twice, E three times | 3,628,800 | 151,200 |
| MISSISSIPPI | 11 | I four times, S four times, P twice | 39,916,800 | 34,650 |
| THE CLASSROOM | 12 | S twice, O twice | 479,001,600 | 119,750,400 |
Read the bottom two rows together. MISSISSIPPI is shorter than THE CLASSROOM by one letter but has 3,456 times fewer arrangements, purely because its letters repeat so heavily. Length sets the ceiling, repetition decides how much of it you actually get.
Frequently asked questions
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See also
Generator verified by the LiczGrupa.pl team
Content, formulas and results have been reviewed for accuracy and relevance by our team of specialists.
Reviewed by: Patryk Matyjasik