Posted by **Joseph** on Sunday, June 30, 2013 at 1:20pm.

In how many ways can I place 5 different beads on a bracelet if flipping or rotating the bracelet does not change the order of the beads?

- Math (Combinatorics) -
**Count Iblis**, Sunday, June 30, 2013 at 2:39pm
The symmetry group here is D_5, see here:

http://en.wikipedia.org/wiki/Dihedral_group

So, you have 10 different rotations and reflections (the identity, i.e. doing nothing is one of these operations).

If you don't take into account this symmetry, you would have had 5!=120 possibilities. Applying different elements of D_5 always gives you a different configuration (this follows from the fact that you have 5 different beads), so the number of different configurations that can't be obtained from each other by applying a rotation or reflection is 120/10 = 12.

If the beds are not all different, then it can happen that two different elements of D_5 applied to the same configuration yield the same result, dividing by 10 then won't give the correct result. In that case, you have to apply Pólya enumeration theorem:

http://en.wikipedia.org/wiki/P%C3%B3lya%27s_enumeration_theorem

- Math (Combinatorics) -
**Joseph**, Sunday, June 30, 2013 at 2:56pm
Awesome, thanks!

## Answer this Question

## Related Questions

- MATH HELP HELP HELP HELP HELP - (a)Sarah wants to make a bracelet. She needs ...
- MATH HELP HELP HELP HELP HELP - (a)Sarah wants to make a bracelet. She needs ...
- math discrete - (a)Sarah wants to make a bracelet. She needs some beads and ...
- Math - Red and blue beads are being strung to make a bracelet. How many ...
- math - A bracelet is made of yellow, green, blue, purple and red beads in that ...
- math - Hey someone use 192 beads to make a necklace and bracelet it takes 5 ...
- math - Milky uses 192 beads to make a bracelet and a necklace.It takes 5 times ...
- Math - mollly uses 192 beads to make a necklace and a bracelet. it takes 5 times...
- math - mollly uses 192 beads to make a necklace and a bracelet. it takes 5 ...
- math - Milky uses 192 beads to make a bracelet and a necklace.It takes 5 times ...