How many ways can 8 friends be arranged around a circular dinner table?  Answers:  A) A)16  B) B)48  C) C)96  D) D)5040  E) E)720
The number of arrangements of n distinct objects in a row is given by n!n!.   The number of arrangements of n distinct objects in a circle is given by (n−1)!(n−1)!.   The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:   n!n=(n−1)!n!n=(n−1)!.   So, the answer is (8 - 1)= 
<gadget id="calculator">(8 - 1)</gadget>
<output>7</output>
7!= 5040.   Answer: 5040.
<result>D</result>
How many ways can 8 friends be arranged around a circular dinner table?