I recently came upon a comment in the mathematics overflow stating that the infinite string of pi was similar to The Library of Babel. This library is a universe containing every possible combination of a 410 page book. There are a finite number of books and every book is unique. After doing a little digging, I found a website that allows a user to search for a specific string in the library and see how many books contain that string. Since the website was only for entertainment purposes, the number of matches changes every page refresh, even with the same search.
This got me thinking, is it possible to calculate how many books contain a give string? I came up with a formula, but I'm not entirely sure if it is correct.
General Information
Pages: 410
Letters Per Page: 3200
Max Length of Search String: (410 * 3200)
Total Characters: 30 (English Alphabet, space, comma, period, question mark)
Total Books: $30^{(3200*410)}$
Books With Search String:
$m = $ Max Possible Length of Search String = (410 * 3200)
$l = $ Length of Input Search String
$\sum_{x=0}^{m - l}\left\{x!*30(m-l + 1)\right\}$