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Math Help - combinations

  1. #1
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    combinations

    In how many ways can the letters in "mississippi" be arranged such that there are no consecutive s's?
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  2. #2
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    Quote Originally Posted by jmedsy View Post
    In how many ways can the letters in "mississippi" be arranged such that there are no consecutive s's?
    sorry , grandad corrected .
    Last edited by mathaddict; January 22nd 2010 at 07:14 AM.
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  3. #3
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    Hello jmedsy
    Quote Originally Posted by jmedsy View Post
    In how many ways can the letters in "mississippi" be arranged such that there are no consecutive s's?
    If, to begin with, we ignore the 4 s's, there are \frac{7!}{4!2!} arrangements of the remaining 7 letters, which have 4 repeated i's and 2 repeated p's.

    Now imagine that these 7 letters are arranged with a space in between each, and an additional space at each end. That's 8 spaces in all. 4 of these 8 spaces must be chosen to contain an s; and there are \binom84 ways of doing this.

    So I reckon the answer is:
    \binom84\times\frac{7!}{4!2!}=7350 ways.
    Grandad
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  4. #4
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    Quote Originally Posted by Grandad View Post
    Hello jmedsyIf, to begin with, we ignore the 4 s's, there are \frac{7!}{4!2!} arrangements of the remaining 7 letters, which have 4 repeated i's and 2 repeated p's.

    Now imagine that these 7 letters are arranged with a space in between each, and an additional space at each end. That's 8 spaces in all. 4 of these 8 spaces must be chosen to contain an s; and there are \binom84 ways of doing this.

    So I reckon the answer is:
    \binom84\times\frac{7!}{4!2!}=7350 ways.
    Grandad
    The book agrees; thanks guys
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