The problem statement implies each subject category will remain together as a group.  If we further assume that "in that order" means the same as "left to right" then there are:



   3! * 4! * 3! * 5!  = 6 * 24 * 6 * 120 = 103680 ways to arrange the books.





Details/insights:

For N unique objects, there are N! arrangements that are unique.



examples:

Two objects AB can be arranged as AB or BA  (2! = 2)

Three objects ABC can be arranged as ABC, ACB, BAC, BCA, CAB, or CBA  (3! = 6)

etc.



 

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