In a wedding banquet, guests are seated in circular table for four. In how many ways can the guests be seated?
We have learned that the number of permutations of 
However, circular arrangement is slightly different. Take the arrangement of guests A, B, C, D as shown in the first figure. The four possible seating arrangements are just a single permutation: in each table, the persons on the left and on the right of each guest are still the same persons. For example, in any of the tables, B is at the left hand side of A and D is at the right hand side of A. In effect, the four linear permutations ABCD, BCDA, CDAB, and DABC are counted as one in circular permutations. That implies that the number of linear permutations of 4 persons is four times its number of circular permutations. Since the number of all possible permutations of four objects is 4!, the number of cirular permutations of four objects is 
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