Suppose that I have an unlimited supply of identical math books, history books, and physics books. All are the same size, and I have room on a shelf for 8 books. In how many ways can I arrange eight books on the shelf if no two books of the same type can be adjacent?
First book can be any of 3
next book can only be 1 of 2 (so as not to match
next book can only be 1 of 2
3 * 2^7 = 384 my guess !