In how many ways can 3 novels, 2 mathematics books, and 1 chemistry book be arranged on a bookshelf if
(a) the books can be arranged in any order? Since there aren't any restrictions, we have 3+2+1=6! = 720 possible arrangements.
(b) the mathematics books must be together and the novels must be together? The Math books are bundled so it's 2! The novels are bundled so it's 3! And since we have three objects: math, novel, and chemistry book, we have 2!3!3!=72
(c) the novels must be together, but the other books can be arranged in any order?

Question

In how many ways can 3 novels, 2 mathematics books, and 1 chemistry book be arranged on a bookshelf if 
(a) the books can be arranged in any order? Since there aren't any restrictions, we have 3+2+1=6! = 720 possible arrangements.
 (b) the mathematics books must be together and the novels must be together? The Math books are bundled so it's 2! The novels are bundled so it's 3! And since we have three objects: math, novel, and chemistry book, we have 2!3!3!=72 
(c) the novels must be together, but the other books can be arranged in any order?

Zarkon · Answer

looks like you are getting it.