John must arrange 3 different physics books and 3 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?
Choose one.
A) 6 B) 9 C) 36 D) 120 E) 720
First place the maths book -   since all are different books, they can be arranged in 3! ways - 6 ways...   next we have 4 places for physics book, but leftmost is not a valid place as left is always maths..   _M_M_M_, but valid ways are M_M_M_   so 3 places for 3 books - again 3! ways...   Total = 3!∗3!=36   ANSWER:36
<result>C</result>
John must arrange 3 different physics books and 3 different mathematics books on one shelf. If the first book on the leftmost side is a mathematics book and no physics book is next to another physics book. How many different arrangements exist?