• Support PF! Buy your school textbooks, materials and every day products Here!

Combinatorics Circular Arrangement

  • Thread starter click
  • Start date
  • #1
10
0

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?
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
not quite, consider the case when all 9 places have the same robot type, linking the circle doe snot make this equivalent to any other arrangements and there will not by any repetitions, so you need to be a little more careful with counting repeated sequences
 

Related Threads on Combinatorics Circular Arrangement

Replies
8
Views
6K
Replies
3
Views
639
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
516
  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
1K
Top