7 people sit at the round table. In how many ways can we sit them so that Bob and Bill don't sit opposing each other?  Choose the most appropriate option.
A) 400
B) 420
C) 440
D) 460
E) 480
7 People: Bob,Bill,Red,Blue,White,Pink,Purple   Round Table: T   7 Chairs: 1,2,3,4,5,6,7   Let chairs 1 and 4 be opposite each other;   Bob is sitting on 1 and Bill is sitting on 4;   The rest of the people on 2,3,5,6,7 - can rearrange themselves in 5! ways   Now, Bill and Bob swap their positions;   Bob is sitting on 4 and Bill is sitting on 1;   The rest of the people on 2,3,5,6,7 - can rearrange themselves in 5! ways   Thus total number of ways in which Bob and Bill are sitting opposite each other = 2*5! = 120*2= 
<gadget id="calculator">120*2</gadget>
<output>240</output>
240   We have to find in how many ways they are NOT sitting opposite; subtract 240 from the total number of possible arrangements;   In circular permutation, Total number of arrangements of n people= (n-1)!   Here number of people = 7   Arrangements = (7-1)= 
<gadget id="calculator">(7-1)</gadget>
<output>6</output>
6!= 720   Number of ways Bob and Bill are NOT sitting opposite = 720-240= 
<gadget id="calculator">720-240</gadget>
<output>480</output>
480.   Answer: 480
<result>E</result>
7 people sit at the round table. In how many ways can we sit them so that Bob and Bill don't sit opposing each other?