document.write( "Question 1024774: There are 11 guests in a party
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\n" ); document.write( "2)In how many ways can the guests be seated at a round table with 15 identical seats? \n" ); document.write( "

Algebra.Com's Answer #640180 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "There are 11 guests in a party
\n" ); document.write( "1)In how many ways can the guests be seated at a round table with 15 numbered seats?
\n" ); document.write( "2)In how many ways can the guests be seated at a round table with 15 identical seats?
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document.write( "1.  The first guest can choose any of 15 seats.\r\n" );
document.write( "    The second guest can choose any of 14 remaining seats.\r\n" );
document.write( "    . . . . \r\n" );
document.write( "    The 11-th guest can choose any of (15-10) = 5 seats.\r\n" );
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document.write( "    In all, there are 15*14*13* . . . *5 =  ways/options.\r\n" );
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document.write( "2.  If the seats are non-numbered (i.e. identical), we can not and do not make distinguish \r\n" );
document.write( "    between configurations that differ by the turning / circular translation of all seats around the table \r\n" );
document.write( "    in 1, 2, 3, . . . , 15 positions. So, we need to divide  by 15.\r\n" );
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document.write( "    Thus the answer is . = 14*13*12* . . . *5.\r\n" );
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