5 different mathematics books, 4 different French books and 2 different biology books are to be arrange on a shelf. How many different arrangements are possible, if1. The books in each particular subject must all stand together? 2. Only the mathematics books must stand together.

Problem 1A = 5! = 5*4*3*2*1 = 120 ways to arrange the math booksB = 4! = 4*3*2*1 = 24 ways to arrange the French booksC = 2! = 2*1 = 2 ways to arrange the biology booksD = 3! = 3*2*1 = 6 ways to arrange the three blocks of books, each block a different subjectE = A*B*C*D = 120*24*2*6 = 34560 different ways to arrange the books such that the subjects stick together-------------Answer: 34560========================================Problem 2Group all the math books to form one "book". This is the same as taking out the 5 math books and replacing it with one single math book. This single math book acts as a placeholder for all of the five books together as one block.We have1 math "book"4 French books2 biology booksSo there are 1+4+2 = 7 "books" total and 7! = 7*6*5*4*3*2*1 = 5040 different ways to arrange those "books"Within the math block of books, there are 5! = 120 ways to arrange things. So overall we have 120*5040 = 604800-------------Answer: 604800