Question

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.)

Answer 1

@KlOwNlOvE

Answer 2

use Burnside's lemma

Answer 3

I think it would be (6-1)!/((2!)(2))
(n-1)!/2 is the formula for permutation on a ring, and in any given line permutation if there are repetitions you divide by the number of repetitions factorialed...
like in permutations of "bookkeeper" it would be 16!/(2!)(2!)(3!) because the o's repeat twice, k's repeat twice, e's repeat three times
So that's why i divided by 2! as well
Double check that answer if you can and see if that makes sense to you... I'm a little rusty on the statistics :P