The librarian has 8 different math books, 4 different English books, and 5 different science books. (a) The librarian wants to rearrange all the books in the line on a single shelf. How many ways are there to rearrange the books so that all the math books must be next to each other in the arrangement? (b) How many ways are there to rearrange the books on a single shelf so that the books may be in any order, but the science books must be separated from one another? (i.e. Avoiding the case where you have at least two graph theory books next to each other in the arrangement.)