we know that there are 5 different topics contining 4 copies (same book) each.
Total ways to arrange all books (we will ignore the fact that there are copies). = 20!
we know that 4 books are the same so we will have to "remove" repetition from 20!
4! (removing set one) * 4! (removing set two) * 4! (removing set three) * 4! (removing set four) * 4! (removing set five).
hence: 20!/4!*4!*4!*4!*4! = 20!/4!^5
the answer is (C).
to better understand lets think about 3 balls - 2 red (R1&R2) and 1 blue (B1). the total ways to arrange the balls is 3! = 6
but now we want to remove all the places that R1R2=R2R1 becuase that is the same thing !! (replacing red and red is the same).
since we have 2 reds in one repeating set (reds) we will remove repetition in 2!
so the outcome is 3!/2! = 3 , try to remove from the table above all the places that R1R2=R2R1 and you will get 3.