Question

Alarge library has 1680 racks. lf there are 12,80,160 books to be arranged,find out the number of books that can be arranged in each rack

Answer 1

The number is probably impractically large as it starts to be impossible to consider every variable.  Let us consider just the first book.  There are 5 possible books you can place on the shelf first (let's go from left to right).  Now there are many ways to arrange that book.  It can be vertical and arranged in one of at least 4 ways such that the spine is facing in or out and the title can be either upside down or right side up.  Now it can also be horizontal on the shelf.  Provided it doesn't have to be square to the shelf it can be arranged in an almost infinite number of ways.  If you limit it to 1-degree increments it can be placed flat in any of 360 ways on its face and 360 more on its back cover.  Now if you allow the book to be opened it can be opened to any page and arranged in any of the 760 orientations allowed when it was closed.  So if the book has 300 pages you have at least  225,000 possible arrangements for just that first book no matter which of the 5 you choose.