Question

NEED HELP ON PROBABILITY QUESTION:

Answer 1

Answer is not 72 or 360, i've tried both.

Answer 2

"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, and rotations are indistinguishable, but turning the bracelet front-to-back is indistinguishable.)"

Answer 3

ok, there are 4 unique charms + 2 identical charms.
i will come back to it later. it isn't a routine circular arrangement problem


let us place one of the unique charms and make it the reference number, 1
the possible distinct placements (in a circle) are 2 or 6, 3 or 5 and 4, ie 3 ways
the remaining 4 unique charms can be placed in 4! ways
thus total # of ways = 3*4! = 72 <---------

Answer 4

"Answer is not 72 or 360, i've tried both."

Answer 5

Lets see is it 24 because there are already the two identical charms so only 4 charms can be rearranged?

Answer 6

I'm thinking, would it be done like this:?
Couldn't you just find the number of ways to have 6 distinguishable charms on a bracelet, if rotations and reflections of the same arrangement are considered the same? Then divide that answer by 2? Because two are indistinguishable really, and they would be interchangeable?

Answer 7

So 6!/2 = 360, then divide by 6, because rotations are the same? And you have to turn the bracelet 6 times to go through all rotations, and get back to where you were?

Answer 8

Then would you divide that by 2? To account for the reflection rule? So i'm thinking it's either 30 or 60.

Answer 9

@saifoo.khan and @Hero can one of you check my logic?

Answer 10

6!/2 (for reflections)/2(for two indistinguishable)/6 (for rotations)

Answer 11

I don't know I'm stuck on this problem too