A circular table is arranged so as to have 9 different robots occupy the table. If there are 5 different types of robots, what is the number of possible arrangements of these robots?
The Attempt at a Solution
If it wasn't a circular table, the answer would be 5^9, I suppose. But since it is circular, there would be repetitions.
<1,2,3,4,5,6,7,8,9> is the same as <2,3,4,5,6,7,8,9,1> and so on.
So I think I need to find the number of repetitions, and subtract it at from 5^9.
There are 9 equivalent seating arrangements for each 'permutation'.
So, is the answer 5^9/ 9 ?
If yes, why isn't it a whole number?