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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.