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Counting and Probability why is this wrong?

  1. May 11, 2012 #1
    Counting and Probability...why is this wrong??

    1. The problem statement, all variables and given/known data

    How many ten letter words can be made from the english alphabet which contain at least one X, at least one Y and at least one Z?



    2. Relevant equations



    3. The attempt at a solution

    1) Choose a place for X (10 ways)
    2)Choose a place for Y(9 ways)
    3)Choose a place for Z(8 ways)
    4)Choose another seven letters from the alphabet (26) with repetitions allowed (267 ways)

    So the number of 10 letter words= 10.9.8.267 where (.) means multiply.

    what is so wrong about this???
     
  2. jcsd
  3. May 11, 2012 #2
    Re: Counting and Probability...why is this wrong??

    Think about this,

    One of your words would have be XXYZCDEFGHI, the bolded X being the one you chose initially. Now, you have another word XXYZCDEFGHI, the bolded again being the X you chose this time. Both are the same words. Apply the same logic to other letters, so many cases in your answer are repeated.
     
  4. May 11, 2012 #3

    Ray Vickson

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    Homework Helper

    Re: Counting and Probability...why is this wrong??

    You double-count the words that have two identical letters, or triple-count the ones with three identical letters, etc.

    RGV
     
  5. May 11, 2012 #4
    Re: Counting and Probability...why is this wrong??

    Ohh now it seems so clear... is it normal to struggle at counting?
     
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