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Thread: Trouble Understanding the difference between permutations and Combinations and some sequence theories?

  1. #1 Trouble Understanding the difference between permutations and Combinations and some sequence theories? 
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    Ok so first question what is the difference between permutations amd combinations? second I don't under stand how to get a working formula for arithmitic, and geometriv series... can someone help me please?


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    Moderator Moderator Cogito Ergo Sum's Avatar
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    I will only address the first part of your O.P., because I do not understand the second part.

    A permutation is:
    Quote Originally Posted by Wolfram MathWorld
    is a rearrangement of the elements of an ordered list into a one-to-one correspondence with itself. The number of permutations on a set of elements is given by
    A combination is:
    Quote Originally Posted by Wolfram MathWorld
    [t]he number of ways of picking unordered outcomes from possibilities.

    I will illustrate these two concepts with an example:

    Suppose I have a box. In this box, there are 4 balls. Each of them is labeled with a number (1 to 4).
    A permutation would be a certain rearrangement of the balls in the box. One arrangement could be 1-2-3-4. Another one could be 1-3-2-4, or 4-2-1-3, etc. The number of permutations (or arrangements of the balls in the box) would be ( is in this case the number of balls: 4), thus:


    (as there are first four balls to pick from the box, then three, and so on)

    A combination is merely picking balls at random from a total of balls in the box, thus:



    It should be noted that the balls are not replaced in the box in both cases.


    Sources:
    Permutation -- from Wolfram MathWorld
    Combination -- from Wolfram MathWorld


    Last edited by Cogito Ergo Sum; December 17th, 2013 at 11:05 AM. Reason: Tex commands added.
    "The only safe rule is to dispute only with those of your acquaintance of whom you know that they possess sufficient intelligence and self-respect not to advance absurdities; to appeal to reason and not to authority, and to listen to reason and yield to it; and, finally, to be willing to accept reason even from an opponent, and to be just enough to bear being proved to be in the wrong."

    ~ Arthur Schopenhauer, The Art of Being Right: 38 Ways to Win an Argument (1831), Stratagem XXXVIII.
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  4. #3  
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    Ok... So permutation is the number of orders outcomes while a combination (n choose m) just the number of possible out comes of n fitting into m?
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    Ok now my other question I know the equation for the sum of s=1+2+3+...n-1+n is equal to n(n+1) divided by 2 but I don't get how we get the equation. And what if the sequence was 1/2 + 2/2 + 3/2 +... N-1/2 + N\2? How do I fin the sum of that by making a formula?
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  6. #5  
    KJW
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    Arithmetic series:











    Last edited by KJW; December 17th, 2013 at 12:10 PM.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by KJW View Post
    Arithmetic series:
    Ok so the arithmetic and geometric formulas work for all?
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  8. #7  
    KJW
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    Geometric series:













    There are no paradoxes in relativity, just people's misunderstandings of it.
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  9. #8  
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    Thank you kwj and corito ergo sum.
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  10. #9  
    Moderator Moderator Cogito Ergo Sum's Avatar
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    Quote Originally Posted by Physicsforall View Post
    Ok... So permutation is the number of orders outcomes while a combination (n choose m) just the number of possible out comes of n fitting into m?

    Yes, that is in essence what I have stated in post #2.
    "The only safe rule is to dispute only with those of your acquaintance of whom you know that they possess sufficient intelligence and self-respect not to advance absurdities; to appeal to reason and not to authority, and to listen to reason and yield to it; and, finally, to be willing to accept reason even from an opponent, and to be just enough to bear being proved to be in the wrong."

    ~ Arthur Schopenhauer, The Art of Being Right: 38 Ways to Win an Argument (1831), Stratagem XXXVIII.
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