In how many ways can 8 people, A, B, C, D, E, F, G, H be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other? Pick one:
A) 384 B) 396 C) 576 D) 40224 E) 696
Number of total arrangements = 8!   Restriction 1= ABC40224 not next to each other --&gt; let say AB and C40224 are considered as one unit, respectively   Restriction 2= AB is not the same as BA + C40224 is not the same as 40224C --&gt; the number will increase by 2*2   Total number of arrangements - Number out of restrictions = Result   8! - (4!*2*2) = 40320 - (24*2*2)= 
<gadget id="calculator">40320 - (24*2*2)</gadget>
<output>40_224</output>
40224   Answer 40224
<result>D</result>
In how many ways can 8 people, A, B, C, D, E, F, G, H be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?