Library of Babel

Jorge Luis Borges' short story Library of Babel conceives of a library comprised of all possible books.  Specifically, all possible permutations of 25 characters (22 letters, comma, period, space) within books with 410 pages.  (Each page has 40 lines; each line has 80 characters).  This set of books would contain all books written so far (spanning multiple volumes if needed), along with all books that could possibly be written in the future.  The majority of the books in the library would be gibberish, of course.

A few questions, ordered from easy to hard:

  • How many books are in The Library of Babel?

  • How much space would this set of books consume (let's ignore the rooms and shelves, and just stack the books, which measure, say, 6 in. x 4 in. x 1.5 in. )?

  • What proportion of the books would read coherently from start to finish?

In this library, there would be a book explaining the solutions to each of these questions!