Question 1132665
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<pre>
From the dictionary 

    <A HREF=https://dictionary.cambridge.org/us/dictionary/english/bracelet>https://dictionary.cambridge.org/us/dictionary/english/bracelet</A> 

    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 <U>THIS WAY</U>


    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!/7}}} = 6! = 1*2*3*4*5*6 = 720.    <U>ANSWER</U>


It is not 7!, as it would be in linear case !
</pre>

Solved.


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<U>The lesson to learn from my post is THIS</U> :


<pre>
    This problem is the same as other classic formulation:


        In how many ways 7 people can be sitting around a circular table ?
</pre>


See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =https://www.algebra.com/algebra/homework/Permutations/Persons-sitting-around-a-circular-table.lesson>Persons sitting around a cicular table</A> 

in this site.