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Math Help - Permutations and Combinations

  1. #1
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    Permutations and Combinations

    I'm having some issues with the word problems. Can you show me how to do them.

    Deturmine the number of difforent arrangements using the letters of the word ACCESSES that:
    A. Begin with exactly two S's.
    B Begin with at least two S's.
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  2. #2
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    Re: Permutations and Combinations

    Quote Originally Posted by Twinkie View Post
    Deturmine the number of difforent arrangements using the letters of the word ACCESSES that:
    A. Begin with exactly two S's.
    B Begin with at least two S's.
    First, do you understand the total number of ways to arrange ACCESSES is \frac{8!}{(2!)^2\cdot(3!)} and why?

    If not, you must start there

    Then the answer to part a) is just the number of ways to arrange ACCEES minus the number of ways to arrange ACCEE.

    You tell us why that is true.
    Thanks from Twinkie
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  3. #3
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    Re: Permutations and Combinations

    Yes, I understand that ACCESSES is 8!/ 2x2x3! ,because there is 8 letters and two C's, 3 S's, and 2 E's.
    So for A, I count all the S's as one in the top half of the equaision like 6!/2x2 ( Now I know what I was doing wrong befor, I was counting the S's as 2 not 1). Then I subtract the equasion without any S's ,So 5!/2x2 ,with the first answer to get the final answer. To get 150, I finally got it right. Thankyou so much!
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