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Math Help - How many bijections [4]--->[4] have no fixed points

  1. #1
    Member oldguynewstudent's Avatar
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    How many bijections [4]--->[4] have no fixed points

    Last of the fixed point problems!

    How many bijections [4] \rightarrow[4] have no fixed points?

    I wrote it out and found 9, and since there are 4! bijections or _4P_4 of [4] \rightarrow[4], I am looking for a formula.

    The only one that makes sense is (n-1)^{n-2}.

    Is that the correct formula? Thanks
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    Member oldguynewstudent's Avatar
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    Thank you very much! This confirms my answer of 9. I'm still trying to decipher formulas but my textbook also mentions derangements.
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    Quote Originally Posted by oldguynewstudent View Post
    Thank you very much! This confirms my answer of 9. I'm still trying to decipher formulas but my textbook also mentions derangements.
    If you don't mind me asking, what textbook are you using?
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  5. #5
    Member oldguynewstudent's Avatar
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    Combinatorics A Guided Tour by David R. Mazur. It's new, first edition.
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