If f is a function and f(i) = i then we call i a fixed point of f.

a) How many functions [5]$\displaystyle \rightarrow$[5] have at least one fixed point?

I have been working on this for hours! I've written out [3]$\displaystyle \rightarrow$[3], and [4]$\displaystyle \rightarrow$[4].

I came up with this bizzare formula but I am sure it is incorrect. Please help!

$\displaystyle [\sum_{k=0}^{n-3}(n-k)(n-2)]+1$