How many different arrangements of A, B, , D, and E are possible where A is not adjacent to B and D is not adjacent to E? Choices
A) 96	B) 48	C) 8	D) 30	E) 1
So you have A,B,,D,E   five possible ways to arrange it = 4! = 24   AB cannot be adjacents neither DE:   (AB),,D,E = 3! = 6x 2(because it can be (AB) or (BA) ) = 12   A,B,,(DE) = 3! = 6 x 2 = 12   To get rid of the double counting:   (AB),(DE) = 2! x 4 = 8   (Four possible ways to arrange it)   24 -12-12+8= 
<gadget id="calculator">24 -12-12+8</gadget>
<output>8</output>
8 possible ways   8
<result>C</result>
How many different arrangements of A, B, , D, and E are possible where A is not adjacent to B and D is not adjacent to E?