SOLUTION: there are 7 people at a round table with 5 seats. how many arrangements are possible? this is circular permutations of algebra 2. Please help. i don't know how to solve it. Thank

Regarding people sitting at a round table, circular permutations differ from convectional permutations in this:

   any two permutations/arrangement of the people around the table that are obtained one from the other by "rotation" 
   in the angle around the table are considered as equivalent or indistinguishable. 

If there are n people sitting around a table, then the number of "rotations" is n (rotations by the angle , , , . . . ).

Therefore, the number of circular permutations of n objects is . =  = (n-1)!.


The number of circular permutations of n objects taken m at a time, is 

.


In your case the number of circular permutations is 

 = 7*6*4*3 = 504.


Is it your school math assignment?

If so, then it is for the first time I see such theme in the school math.