SOLUTION: find the number of distinguishable permutations that can be made from the letters of the word ANTARCTICA

Question 1110776: find the number of distinguishable permutations that can be made from the letters of the word ANTARCTICA
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.

There are 10 letters (symbols) in the word, in all.


Of them, there are 

    - 3 repeating (identical) "A", 

    - 2 repeating (identical) "T".

    - 2 repeating (identical) "C".


The number of distinguishable permutations is  P  =  = 151200.


3! in the denominator accounts for repeating "A",

2! in the denominator accounts for repeating "T",

3! in the denominator accounts for repeating "C".

See 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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