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Math Help - [SOLVED] Functions

  1. #1
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    [SOLVED] Functions

    How many functions are there from {0,1,...,n-1} to {0,1} where n > 1 that:
    1)are one to one
    2)assign 0 to both 0 and n-1.
    3)assign 1 to exactly one positive integer less than n-1.


    Here is what ive done:

    1) n C 2 = x, and since you can arrange it in 2 ways, then 2x.
    For e.g: 2 C 2 = 1, 1 x 2 = 2 one -to-one functions.

    2)Im not sure. Would like some help. There will be at least 1 function
    (0 - 0). But confused about n-1!

    3) im not sure what its asking, im confused. Taking a guess ill say it is
    n-1 C 1.


    Can i please have some help on 2 and 3 please and a check if im correct on Q1.
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  2. #2
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    Quote Originally Posted by kurac View Post
    How many functions are there from {0,1,...,n-1} to {0,1} where n > 1 that:
    1)are one to one
    2)assign 0 to both 0 and n-1.
    3)assign 1 to exactly one positive integer less than n-1.
    The answers are:
    1) none
    2) none
    3) n-2 if n\ge3.
    WHY?
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  3. #3
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    Ok then, didnt expect that. But your assuming for total, which would make your Q1 correct. But for total and partial, i think it would be what i had.
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