Pairs who swap hats

Five people check their hats and, at the end of the night, the hats are handed back in a uniformly random order (a random permutation). What is the expected number of pairs of people who exchange hats - that is, unordered pairs $\{i,j\}$ where $i$ gets $j$'s hat and $j$ gets $i$'s hat? Give a decimal to four places.