# Thread: How many bijections [4]--->[4] have no fixed points

1. ## 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

2. Thank you very much! This confirms my answer of 9. I'm still trying to decipher formulas but my textbook also mentions derangements.

3. Originally Posted by oldguynewstudent
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?

4. Combinatorics A Guided Tour by David R. Mazur. It's new, first edition.