SOLUTION: What is the total number of different 10-letter arrangements that can be formed using the letters in the word ABSTEMIOUS?

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Question 1158097: What is the total number of different 10-letter arrangements that can be formed using the letters in the word ABSTEMIOUS?
Answer by ikleyn(52776) About Me  (Show Source):
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There are 10 letter in the word.


They all are UNIQUE, except one letter " S ", which has multiplicity of 2.


Therefore, the number of all distinguishable arrangements of the letters is  10%21%2F2%21 = 3%2A4%2A5%2A6%2A7%2A8%2A9%2A10 = 1814400.    ANSWER


2! in the formula serves to account for repeation letter " E ".

Solved.

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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.