document.write( "Question 1117736: How many ways can 6 people work at 3 different offices if 2 people are in each office and 2
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Algebra.Com's Answer #732900 by ikleyn(52778) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "            The way to solve this problem is to calculate the number of all possible configurations without the imposed constraint, \r
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\n" ); document.write( "\n" ); document.write( "1.   Calculating the number of all possible configurations without the imposed constraint.\r
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document.write( "    You can create the first pair by   =  = 15 ways and place this pair to any of the 3 offices;\r\n" );
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document.write( "    so you have 15*3 = 45 ways to do it.\r\n" );
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document.write( "    You can create the second pair from remaining 4 people by   =  = 6 ways and to place it to any of remaining 2 offices.\r\n" );
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document.write( "    You have 6*2 = 12 ways to do it.\r\n" );
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document.write( "    With the third pair, you have nothing to select - NEITHER the pair NOR the office.\r\n" );
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document.write( "    So, working without the constraint, you have 45*12 = 540 ways to do it.\r\n" );
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document.write( "    You just have this \"prohibited\" pair of the two persons who hate each other.\r\n" );
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document.write( "    So you need calculate how many pairs you can create with remaining 4 people and distribute them.\r\n" );
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document.write( "    You can create the first pair in   =  = 6 ways and place it to any of 3 offices:  6*3 = 18 options.\r\n" );
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document.write( "    Regarding the second pair, you just have no choice (you have only one selection) and can place this pair to any of 2 remaining offices.\r\n" );
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document.write( "    In all, you have 18*2 = 36 \"prohibited\"  options under the restriction.\r\n" );
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document.write( "    So, the final answer is:  540 - 36 = 504  ways.\r\n" );
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