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Math Help - Functions and sets

  1. #1
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    Functions and sets

    Can somebody explain to me how to do the follow please:

    1)Compute the number of functions from a set with n elements to a set with m elements.

    and secondly,

    2) compute the number of one-to-one functions (injections) from a set with n elements to a set with m elements.


    Can someone tell me how they get the answer, i really want to understand this.

    Thanks guys.
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  2. #2
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    1) Each element in the domain can be mapped to one of m elements. m choices for the first, m choices for the 2nd, ... , m choices for the nth. So n^m.

    2) The first element can be mapped to m different elements, the 2nd to m-1, the 3rd to m-3 .. etc
    So n*...*(n-m+1) = n! / m!
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  3. #3
    Senior Member pankaj's Avatar
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    2.
    n(n-1)(n-2)(n-3)......(n-m+1)=\frac{n!}{(n-m)!}


    Here's another one:
    How many ONTO functions can be constructed
    Last edited by pankaj; May 28th 2009 at 07:52 AM.
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  4. #4
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    Whoops, my mistake. Pankaj is correct.
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  5. #5
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    thanks guys, that is great!
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