John must arrange 3 different physics books and 4 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 the correct answer
A) 6  B) 9  C) 36  D) 120  E) 144
First Place, is reserved for Math book. There are 3 Math books which can be arranged in3 ways   Restriction comes into playhysics book cannot be together. Hence, the maththe physics books take alternate places   Second Place, Physics Book - in 4 ways   Third Place, Math Book - in 2 ways (only 2 books left)   Fourth Place, Physics - in 2 ways (only 2 Physics book left)   Rest two places can be arranged in one way only.   Total no of ways = 4*3*3*2*2*1*1= 
<gadget id="calculator">4*3*3*2*2*1*1</gadget>
<output>144</output>
144 ways   144
<result>E</result>
John must arrange 3 different physics books and 4 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?