document.write( "Question 1132665: In how many ways can 7 charms be placed in a bracelet which has no clasp? \n" ); document.write( "
Algebra.Com's Answer #749760 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "From the dictionary \r\n" );
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document.write( "    https://dictionary.cambridge.org/us/dictionary/english/bracelet \r\n" );
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document.write( "    https://dictionary.cambridge.org/us/dictionary/english/bracelet\r\n" );
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document.write( "you can read that a bracelet is a piece of jewelry that is worn around the wrist or arm.\r\n" );
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document.write( "In this definition, it is important for us now that a bracelet has a circular form like a closed line.\r\n" );
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document.write( "So, the question can be EQUIVALENTLY reformulated in THIS WAY\r\n" );
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document.write( "    In how many ways can 7 charms be placed along a circumference of a circle ?\r\n" );
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document.write( "In such problems the placements that obtained one from the other by rotation of a circle by some angle are considered as INDISTINGUISHABLE.\r\n" );
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document.write( "Therefore, with each concrete placements, 6 others that obtained from the original placement by rotation, are considered as EQUIVALENT.\r\n" );
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document.write( "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\r\n" );
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document.write( "It is not 7!, as it would be in linear case !\r\n" );
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from my post is THIS :\r
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document.write( "    This problem is the same as other classic formulation:\r\n" );
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document.write( "        In how many ways 7 people can be sitting around a circular table ?\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Persons sitting around a cicular table \r
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