How many different arrangements of A, B, C, D, and E are possible where A is not adjacent to B and D is not adjacent to E?  Choose the correct answer
A) 96	B) 48	C) 32	D) 30	E) 1
So you have A,48,C,D,E   five possible ways to arrange it = 5! = 120   A48 cannot be adjacents neither DE:   (A48),C,D,E = 4! = 24 x 2(because it can be (A48) or (48A) ) = 48   A,48,C,(DE) = 4! = 24 x 2 = 48   To get rid of the double counting:   (A48),C,(DE) = 3! x 4 = 24   (Four possible ways to arrange it)   120 -48-48+24= 
<gadget id="calculator">120 -48-48+24</gadget>
<output>48</output>
48 possible ways   ANSWER:48
<result>B</result>
How many different arrangements of A, B, C, D, and E are possible where A is not adjacent to B and D is not adjacent to E?