My friend lost 2 charms off her 7-charm bracelet. For her birthday, I bought her a new charm to replace one of the lost ones. Unfortunately, I messed up and got her a duplicate of one of the charms she still has. How many distinguishable ways can she put her 6 charms on her bracelet? (Two of the charms are the same, rotations are indistinguishable, and turning the bracelet front-to-back is indistinguishable.)

Guest Mar 29, 2015

#1**+11 **

I think it is $$\frac{5!}{2!}=60$$ that should take care of the 2 the same and the rotations.

If they were set in a line it would be 6!/2 but you always take one off when they are set in a circle.

But since you also have to take care of the turning front-to-back you might need to divide this by two.

So the answer might be 30

Melody Mar 29, 2015