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Math Help - permutation question

  1. #1
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    permutation question

    I am trying to clear something up in my head, if I have the below

    set1 of {A,B,C,D,E,F,G}
    set2 of {w,x,y,z}

    My question how many ways can set1 map to set2, well 6X4=24 ways

    but what if I had 10 or 10million sets of 'x,x1,x2,xbla' number of elements then what formula would I have to use for an ordered mapping set1 ->set 2>set3

    just multiply the number of elements in each set together?

    Could someone explain briefly the approach for this on permutations and combinations, with and without repetition.

    Many thanks
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  2. #2
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    Re: permutation question

    Quote Originally Posted by benjamin872 View Post
    I am trying to clear something up in my head, if I have the below
    set1 of {A,B,C,D,E,F,G}
    set2 of {w,x,y,z}

    My question how many ways can set1 map to set2, well 6X4=24 ways this is incorrect
    The correct answer is 4^7. Let \|A\| stand for the number of in the finite set A.

    The number of functions from A\to B is \|B\|^{\|A\|} That is the total number.

    Quote Originally Posted by benjamin872 View Post
    Could someone explain briefly the approach for this on permutations and combinations, with and without repetition.
    The only way to do it without repetition is if \|A\|\le\|B\|~.
    Last edited by Plato; November 24th 2013 at 12:50 PM.
    Thanks from benjamin872
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