A math teacher uses four algebra books, two geometry books, and three pre-calculus books for reference. In how many ways can the teacher arrange the books on the shelf if books coiver the same subject matter are kept together?

Answer 1

There are 3! =6 ways to order the three separate topics.

For each of these ways, there are 4! ways to arrange the algebra books, 2! ways for the geometry books, and 3! ways for the pre-cal books.

So, in all, there are 3! 4! 2! 3! = 6*24*2*6 = 1728 ways.

Note that if the subjects did not have to be kept together, there would be 9! = 362880 ways.