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Math Help - Arranging letters...

  1. #1
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    Red face Arranging letters...

    Hey I need help with this seemingly easy question with arranging letters:

    Q1) How Many ten-letter words can be formed from the letters of PARRAMATTA? How many nine-letter words? How many 8-letter words?

    Thanks
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  2. #2
    Member billym's Avatar
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    google "counting anagrams"
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  3. #3
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    hmmm...most of the links from google are about programing anagram solvers, etc. Not really about the counting problem here.
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  4. #4
    Member billym's Avatar
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    The very first result from google is

    this

    It gives the equation \frac{n!}{n_1!n_2!...n_k!} where n is the length of the word, n_1 is the number of times the first letter is in the word, and so on...

    So for PARRAMATTA its \frac{10!}{4!2!2!}
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  5. #5
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    Hey sorry, I understand how to do it for ten letter words. That is, the number of annograms for the word. However I dont understand how to the rest of the quetion. 9 letter words and then 8 letter words from the original 10 letter word PARRAMATTA.
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  6. #6
    Member billym's Avatar
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    There are 5 different letters in the word. Dump one of one type and repeat the above process for 9 letters. Then dump one of a different type...

    For 8 letters, think of what you would be left with if you got rid of PA, then PR, then PM...
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