The word 'dermatoglyphics' refers to the study of patterns on the skin. It's of interest to word-puzzle enthusiasts (as well detectives; think fingerprints) because at 15 letters it weighs in as one of the longest words in English with no repeated letters.

Imagine we scramble the letters completely at random, to get an anagram: for example 'eymrsopahcdgtli'. Suppose we try many of these anagrams and count the number of letters that are in the same position as they were in the original 'dermatoglyphics'. The count can be anything from 0 to 13, or 15. What will its average value be?