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

Answer:30 ways

Explanation:

Given

there are total of 6 charms out of which 2 are same

total no of ways in which n person can be arranged in a round table is (n-1)!

So 6 charms can be arranged in a bracelet is (6-1)!

Now two charms are same i.e. total no of ways to arrange

`=((6-1)!)/(2)`

`=(5!)/(2)=60 ways`

As rotation are indistinguishable i.e. clockwise become anti-clockwise therefore

total no of ways are
`=(60)/(2)=30`