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## Homework Statement

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?

## Homework Equations

## 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'.

for example,

<1,2,3,4,5,6,7,8,9>

<2,3,4,5,6,7,8,9,1>

<3,4,5,6,7,8,9,1,2>

<4,5,6,7,8,9,1,2,3>

<5,6,7,8,9,1,2,3,4>

<6,7,8,9,1,2,3,4,5>

<7,8,9,1,2,3,4,5,6>

<8,9,1,2,3,4,5,6,7>

<9,1,2,3,4,5,6,7,8>

So, is the answer 5^9/ 9 ?

If yes, why isn't it a whole number?