Damerau–Levenshtein distance

In every science, in order to reduce calculations, scientists introduce classes, i.e. groups of elements with the same property. By doing so, they don't have to calculate the result for each one of the elements in the group. Instead, there is a general formula that works for all of them.

In our case, we can define the class of the strings of length $n$, in which all the characters are different. Then we consider these strings and their reverses, i.e. the words written in reverse order.

What is the Damerau-Levenshtein distance of a random string from the class mentioned above and its reverse string?

Examples of such pairs of strings: 
"LIVE" and "EVIL"
"VOLUMES" and "SEMULOV"
"012345678" and "876543210"