Permutations vs. combinations

Discussion in 'Math' started by boks, Jan 6, 2009.

  1. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    What's the difference between these two:

    1) The number of permutations of n distinct objects taken r at a time is \frac{n!}{(n-r)!}

    and

    2) The number of combinations of n distinct objects taken r at a time is \frac{n!}{r!(n-r)!}

    ?
     
  2. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    You have surely already noticed that:

    since permutations = \frac{n!}{(n+r)!}

    and combinations = \frac{1}{r!} *\frac{n!}{(n+r)!}

    then combinations = permutations time \frac{1}{r!}

    hgmjr
     
  3. steveb

    Senior Member

    Jul 3, 2008
    2,433
    469
    Can you be more specific as to what you are trying to understand.

    The literal answer to your question is that the difference is
    \frac{n!}{(n-r)!}-\frac{n!}{r!(n-r)!}

    Surely, that is not what you mean. Are you trying to undrstand what the definitions of permutations and combinations are?
     
  4. Mathematics!

    Senior Member

    Jul 21, 2008
    1,022
    4
    permutations - order does matter in counting ABC is different then BCA

    combinations - order doesn't matter if you have to choose 2 elements out of 5 elements.

    Example {A,B,C,D,E} you don't count {A,B,C} different from {B,A,C}
    They are the same

    But permutations would consider them both different and count as 2 .
     
  5. intrepid_atom

    New Member

    Feb 21, 2009
    1
    0
    To support Mathematics!

    combinations = "select"
    Ex: In how many ways you can select 3 letters from A,B,C,D,E?
    5!/(3!2!)
    permutations = "select and arrange"
    Ex: In how many ways you can select 3 letters from A,B,C,D,E and then arrange those 3 letters?
    5!3!/(3!2!) = 5!/2!
     
  6. jamesprx

    Guest

    Permutation is usually understood to be a sequence containing each element from a finite set once..

    Combination is arrangment of elements in any order, to get different possible sequences
     
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