Last of the fixed point problems!

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

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

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

Is that the correct formula? Thanks