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Math Help - how many arrangements?

  1. #1
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    how many arrangements?

    How many arrangements of the word CHARACTERISTIC are there?
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  2. #2
    Super Member Random Variable's Avatar
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    I'm assuming you mean if you use all of the letters.

    If I counted correctly, there are 3 C's, 1 H, 2 A's, 2 R's, 2 T's, 1 E, 2 I's, and 1 S.

    then the number of distinguisable permutations of the 14 letters of "characteristic" is

     \binom{14}{3} \binom{11}{1} \binom{10}{2} \binom{8}{2} \binom{6}{2} \binom{4}{1} \binom{3}{2} \binom{1}{1} = \frac{14!}{3!1!2!2!2!1!2!1!}
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  3. #3
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    ok so the answer is then

    908107200
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