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Dermatoglyphics - A Puzzle

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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?

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Richard Walker

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To be clear, I did not know the answer 24 hours ago. But having read some articles and even written a program I see what is, and could explain it. But I am still surprised by it!

I’m not asking for tight mathematical answers, just guesses or intuitions really. Have a go, you can only be right or wrong.

I will post another hint on Monday.

Richard Walker

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Whoops, forgot hint blush

I'll post an explantion of the solution ...