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Partition of the alphabet

  1. Aug 26, 2011 #1
    Find the number of the partition of the alphabet {A,b.........................Z} of the type (2,2,2,3,3,3,3,4,4)


    So I did 26!/(2!2!2!3!3!3!3!4!4!) = A REALLY BIG NUMBER

    then I took that number and dived it by (3!4!2!) and got 2.344 x10^17 which seems to big to be an answer. So I'm wondering if the number should be that big or did I mess up somewhere
     
  2. jcsd
  3. Aug 26, 2011 #2

    Mark44

    Staff: Mentor

    Shouldn't B be in the alphabet, not b?

    Please clarify what you mean by the terms "number of the partition of the alphabet " and "of the type (2,2,2,3,3,3,3,4,4)".
     
  4. Aug 26, 2011 #3
    yes b is B sorry about that is all 26 of them

    (2,2,2,3,3,3,3,4,4)

    means like AB| CD| EF | GHI|...........|WXYZ
     
  5. Aug 26, 2011 #4

    Dick

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    You should expect to get a really large number. There are lots splitting the alphabet into groups like that. I get the same number, 234481761013500000, if you want to spell it out exactly.
     
  6. Aug 26, 2011 #5
    ok so my answer is right, it just seem to large
     
  7. Aug 26, 2011 #6

    Dick

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    Just out of curiosity, how large would you think it ought to be? I would expect something in the rough ballpark of 26!. And that's similarly large.
     
  8. Aug 26, 2011 #7
    I understand that 26! is large. I was thinking that I must have messed up somewhere when dividing by using the wrong number or something
     
  9. Aug 26, 2011 #8

    Dick

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    No mess up. Good job. Just adjust your intuition. Combinatorial answers to questions with even smallish number of element (like 26) often give huge answers.
     
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