a science teacher is arranging her books on a shelf. she has 4 astrology 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 put together?
Let AAAA be the 4 astronomy books, BBB be the biology books, and CC be the chemistry books. We can group the terms into X, Y, Z repsetivley. Hence we get:
There are 3! ways to rearrange this. However, each of the X can be rearranged 4! ways, and the Y can be rearranged in 3! ways, and the Z can be rearragned in 2! ways.
Hence, our answer is:
4! * 3! * 3! * 2!