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Math Help - Permutation Help!

  1. #1
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    Permutation Help!

    Consider the Permutations of the word SUCCESSFUL ?

    a) How many permutations total?
    b)How many have the 3 vowels adjacent (such as SUUESSFCLC)?
    c)How many permuations have none of the 3 vowels adjacent?
    d)How many permutations start with an S and end with an L?
    e)How many permutations have a consonant as the first letter?
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  2. #2
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    Quote Originally Posted by zackgilbey View Post
    Consider the Permutations of the word SUCCESSFUL ?
    a) How many permutations total?
    \frac {10!} {(3!)(2!)(2!)}
    Now you do some work. Show us some work.
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  3. #3
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    im plugging away at this, and i understand the 10 factorial as well as the (2!) (2!), but not positive on how the 3! was determined. thanks
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    Quote Originally Posted by zackgilbey View Post
    im plugging away at this, and i understand the 10 factorial as well as the (2!) (2!), but not positive on how the 3! was determined. thanks
    Surely this topic is included in your text material: arrangements with repetitions.
    The number of ways to rearrange the word “MISSISSIPPI” is \frac {11!}{(4!)^2(2!)}.
    That is due to the fact there are 11 letters in all, 4 S’s, 4 I’s, and 2 P’s.
    Consider the word “UNUSUAL”. There are there are seven letters in all.
    If we add subscripts U_1NU_2SU_3AL, now the number of ways to rearrange the word is 7!.
    But removing the subscripts makes us divide 3! to account for the fact that is the number of ways to rearrange U_1U_2U_3.
    Last edited by Plato; January 19th 2009 at 02:51 AM.
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  5. #5
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    thanks for the help ive been able to plug right through these except the last one e) im having trouble with how to approach this one as I havent seen this type of question before... any help regarding this would be excellent thanks
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