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Thread: letters

  1. #1
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    letters

    how many arrangements of the letters SWARMED are possible if A and R must be separated by at least 1 letter.

    im night sure if this is a combinations or permutations question.

    this is what i did. i found the total combinations if A and R are together which is 5!. A and R can be A and R or R and A so thats 2! so 5!*2! than total ways of arranging the letters are 7! so 7!- 5!*2! is the answer i get. i dont think this is right.
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  2. #2
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    Re: letters

    Quote Originally Posted by markosheehan View Post
    how many arrangements of the letters SWARMED are possible if A and R must be separated by at least 1 letter.
    The way you want to count these is correct, but your count is off.
    Look at $\boxed{AR},S,W,M,E,D$. There are $6!$ ways to arrange those six items (not 5!).
    So why $7!-2\cdot 6!~???$
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  3. #3
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    Re: letters

    sorry yes 6. 3600 is the right answer.

    do you know when you use permutations vs combinations ? whats the difference
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  4. #4
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    Re: letters

    Same as:
    1234567
    12 or 21 nowhere to be seen!

    lowest: 1324567
    highest: 7654231
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  5. #5
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    Re: letters

    Quote Originally Posted by markosheehan View Post
    do you know when you use permutations vs combinations ? whats the difference
    Permutations are about order while combinations are about content.

    For example, suppose the is a collection of people: a club, a school class, any group.

    If the question asks 'how many ways can four members be selected to plan a party' then we use combinations.
    That is strictly about the content of the committee.

    On the other hand, if we ask 'how many can we select a Pres., VP, Treasurer & Secretary' then we use permutations.
    We are still selecting four people, but in this case order makes a difference.
    Thanks from markosheehan
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