SOLUTION: In how many ways can 7 charms be placed in a bracelet which has no clasp?

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Question 1132665: In how many ways can 7 charms be placed in a bracelet which has no clasp?
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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From the dictionary 

    https://dictionary.cambridge.org/us/dictionary/english/bracelet 

    https://dictionary.cambridge.org/us/dictionary/english/bracelet

you can read that a bracelet is a piece of jewelry that is worn around the wrist or arm.



In this definition, it is important for us now that a bracelet has a circular form like a closed line.



So, the question can be EQUIVALENTLY reformulated in THIS WAY


    In how many ways can 7 charms be placed along a circumference of a circle ?



In such problems the placements that obtained one from the other by rotation of a circle by some angle are considered as INDISTINGUISHABLE.


Therefore, with each concrete placements, 6 others that obtained from the original placement by rotation, are considered as EQUIVALENT.


Therefore, the number of all possible placements of 7 charms in a bracelet is  7%21%2F7 = 6! = 1*2*3*4*5*6 = 720.    ANSWER


It is not 7!, as it would be in linear case !

Solved.

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The lesson to learn from my post is THIS :

    This problem is the same as other classic formulation:


        In how many ways 7 people can be sitting around a circular table ?


See the lesson
    - Persons sitting around a cicular table
in this site.