A set of 3 different Mathematics books, 4 different Physics books, and 2 different English books are arranged on a shelf. If the math textbooks are kept together, then the number of different arrangements possible for the books is
my work:
3 math book: 3! 4 different physics books: 4! 2 different English books: 2!
number of different arrangements is to multiply each = 288 the number of arrangements possible for this book is 288 ways.
Temporarily treat the grouped math books as a single entity. Then you have seven "entities". These can be placed in $7!$ orders on the shelf.
Now "break apart" the math entity. There are $3!$ ways to internally order those math books.
Hence $7! 3! = 30,240$