Entry

Math: Combinatorics: How to calculate total different permutations with repetition? [anagram]

Mar 24th, 2008 22:12
sunny jaswani, Knud van Eeden, http://www.webs4soft.com

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--- Knud van Eeden --- 09 April 2021 - 08:04 pm ----------------------
Math: Combinatorics: How to calculate total different permutations 
with repetition? [anagram]
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The total amount of unique permutations will be a
'permutation with repetition'
You have to divide by the permutations of the repeating elements.
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E.g.
How many unique permutations for the word
 Johnny
You see that the 'n' appears twice.
Thus you have to divide by 2!, or thus 2.
Giving a total of 6! / 2! = 120 / 2 = 60 different permutations.
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E.g.
How many unique permutations for the word
 sos
You see that the 's' appears twice.
Thus you have to divide by 2!, or thus 2.
Giving a total of 3! / 2! = 6 / 2 = 3 different permutations.
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E.g.
How many unique permutations for the word
 cocao
You see that the 'c' appears twice,
and also the 'o' appears twice.
Thus you have to divide by 2! because of the 'c',
and again divide by 2! because of the 'o'.
Giving a total of 5! / 2! / 2! = 120 / 2 / 2 = 30 different 
permutations.
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E.g.
How many unique permutations for the word
 mammalian
You see that the 'm' appears three times,
the 'a' appears three times.
Thus you have to divide by 3! because of the 'm',
and again divide by 3! because of the 'a'.
Giving a total of 9! / 3! / 3! = 362880 / 6 / 6 = 10080 different 
permutations.
hi dear
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Internet: see also:
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BBCBASIC: Windows: Combinatorics: Link: Can you give an overview of 
links?
http://www.faqts.com/knowledge_base/view.phtml/aid/45285/fid/768
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