document.write( "Question 730191: Ten students are to sit on a bench. If two particular student must not sit next to each other, how many sitting arrangement are possible? \n" ); document.write( "

Algebra.Com's Answer #853045 by ikleyn(53418) $\"\"$ $\"About$

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\n" ); document.write( "Ten students are to sit on a bench. If two particular student must not sit next to each other,
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document.write( "With no restrictions, 10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 permutations/arrangements are possible.\r\n" );
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document.write( "With the restriction, we consider the pair of particular students as one block/item.\r\n" );
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document.write( "So, there are 2*9! different unwanted arrangements.\r\n" );
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document.write( "The factor 2 appeared since, two particular students can be ordered in 2 different ways.\r\n" );
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document.write( "So, the number of allowed arrangements is  10! - 2*9! = 3628800 - 2*(9*8*7*6*5*4*3*2*1) = 2903040.\r\n" );
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document.write( "ANSWER.  The number of allowed arrangements is  2903040.\r\n" );
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