A science teacher is arranging her books on a shelf. She has 4 astronomy books, 3 biology books, and 2 chemistry books. How many ways can she arrange these books on the shelf if the books from each subject must be together?
We can arrange the Astronomy books in 4 ! = 24 ways
We can arrange the Biology books in 3 ! = 6 ways
We can arrrange the Chemistry books in 2 ways
And we can arrange the subjects in 3 ! ways = 6
24 * 6 * 2 * 6 = 1728 different ways