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Math Help - Permutation doubt

  1. #1
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    Permutation doubt

    Question
    How many permutations can be made from the letters in the word "Wednesday" if a)4 letters are used at the same time b) all the letters are used

    Attempt
    a) \frac{9!}{(9-4)!} = 3024

    b) Since some letters are alike
     \frac{9!}{1!*2!*2!*1!*1!*1!*1!} =90720


    Am I correct?
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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    Question
    How many permutations can be made from the letters in the word "Wednesday" if a)4 letters are used at the same time b) all the letters are used Attempt
    a) \frac{9!}{(9-4)!} = 3024

    b) Since some letters are alike
     \frac{9!}{1!*2!*2!*1!*1!*1!*1!} =90720
    The answer for part (b) is correct.

    For part (a), there are several cases to consider.
    i) all letters are different.
    ii) use either 'e' or 'd' twice, the others are different.
    iii) have two twice 'eded'
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  3. #3
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    Quote Originally Posted by Plato View Post
    The answer for part (b) is correct.

    For part (a), there are several cases to consider.
    i) all letters are different.
    ii) use either 'e' or 'd' twice, the others are different.
    iii) have two twice 'eded'
    So how would the answer of part A come out ...

    Because I am getting confused or what you are trying to say is that the question is wrong?

    Thank you for your help
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  4. #4
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    For case i) P(7,4)=\frac{7!}{3!}

    For case ii) 2 \binom{5}{2} \left(\frac{4!}{2}\right)

    For case iii) \frac{4!}{(2!)^2}
    Add them up.
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