SOLUTION: How many distinct permutations can be formed using the letters of the word ​"CHARACTER​"?

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Question 1155819: How many distinct permutations can be formed using the letters of the word ​"CHARACTER​"?
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
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How many      distinguishable  arrangements  can be formed using the letters of the word ​"CHARACTER​"?
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In all, there are 9 letters in the word.


Of them, letter "C" has multiplicity 2;

         letter "A" has multiplicity 2;

         letter "R" has multiplicity 2.
 

The rest of the letters are UNIQUE.


The number of distinguishable arrangements of letters is   =  = 45360.    ANSWER


Three times repeated factor 2! in the denominator is to account for three repeated letters "C", "A" and "R" with their multiplicities.


It is a standard method of solving such problems and a standard mantra to pronounce.

Memorize it (!)

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To see other similar solved problems,  look into the lesson
    - Arranging elements of sets containing indistinguishable elements
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.


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