How do you calculate permutations of a word?

ntaraxq 2022-07-05 Answered
How do you calculate permutations of a word?
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Answers (1)

Madden Luna
Answered 2022-07-06 Author has 9 answers
Step 1
For the first part of this answer, I will assume that the word has no duplicate letters.
To calculate the amount of permutations of a word, this is as simple as evaluating n!, where n is the amount of letters. A 6-letter word has 6 ! = 6 5 4 3 2 1 = 720 different permutations.
To write out all the permutations is usually either very difficult, or a very long task. As you can tell, 720 different "words" will take a long time to write out. There are computer algorithms and programs to help you with this, and this is probably the best solution.
Step 2
The second part of this answer deals with words that have repeated letters. One formula is n ! m A ! m B ! ... m Z ! where n is the amount of letters in the word, and m A , m B , ... , m Z are the occurrences of repeated letters in the word. Each m equals the amount of times the letter appears in the word. For example, in the word "peace", m A = m C = m P = 1 and m E = 2 . So the amount of permutations of the word "peace" is: 5 ! 1 ! 1 ! 1 ! 2 ! = 5 4 3 2 1 1 1 1 2 1 = 60
Step 3
I will go through two more examples, but I will ignore every instance of 1! since 1 ! = 1 .
For the word "committee": m C = m O = m I = 1
m M = m T = m E = 2
Permutations: 9 ! 2 ! 2 ! 2 ! = 9 8 7 6 5 4 3 2 1 ( 2 1 ) ( 2 1 ) ( 2 1 ) = 45 , 360
For the word "cheese": m C = m H = m S = 1
m E = 3
Permutations: 6 ! 3 ! = 6 5 4 3 2 1 3 2 1 = 120
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