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Math Help - Combinatorial problem

  1. #1
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    Combinatorial problem

    Can anyone check if my below given questions answer is correct or not...

    (a) How many different strings can be formed by rearranging all the letters of the word MISSISSAUGA? Briefly justify your answer.

    my ans) 9!

    (b) How many of the rearrangements in part (a) contain 4 Sís in a row? Briefly justify your answer.

    my ans) Permutation(8,4)


    Thanks for the help!
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  2. #2
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    Hello, robocop_911!

    Sorry, your answers are wrong . . .


    (a) How many different strings can be formed by rearranging all the letters
    of the word MISSISSAUGA?

    There are 11 letters: . \underbrace{A\;A}_2\;G\;\underbrace{I\;I}_2\:M\;\u  nderbrace{S\;S\;S\;S}_4\;U

    There are: . \frac{11!}{2!2!4!} \:=\:415,800 possible strings.



    (b) How many of the rearrangements in part (a) contain 4 Sís in a row?

    Tape the four S's together.

    Then we have 8 "letters" to arrange: . \underbrace{A\;A}_2\;G\;\underbrace{I\;I}_2\;M\;\b  oxed{SSSS}\;U

    There are: . \frac{8!}{2!2!} \:=\:10,080 arrangements.

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  3. #3
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    By strings, I assume the first one asks for how many arrangements can be made from the word MISSISSAUGA?.

    We have 4 S's, 2 A's, 2 A's.

    \frac{11!}{2!2!4!}=415800


    Now, for the second one:

    Tie the S's together as one big letter. There is 8 places to put them and then arrange the other 7 letters in \frac{7!}{2!2!}=1260 ways.

    \frac{8!}{2!2!}=10080
    Last edited by galactus; June 13th 2008 at 06:23 PM. Reason: Soroban beat me but I can see we concur.
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