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.)

Respuesta :

Answer:30 ways

Step-by-step 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

[tex]=\frac{(6-1)!}{2}[/tex]

[tex]=\frac{5!}{2}=60 ways[/tex]

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

total no of ways are [tex]=\frac{60}{2}=30[/tex]                    

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