document.write( "Question 971491: In how many ways could 14 people be divided into five groups containing, respectively, 1,2,5,4, and 2 people? \n" ); document.write( "

Algebra.Com's Answer #594043 by Edwin McCravy(20055) $\"\"$ $\"About$

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In how many ways could 14 people be divided into five groups containing, respectively, 1,2,5,4, and 2 people?
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document.write( "The only difficulty that is presented here is that we have two groups of 2.\r\n" );
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document.write( "First let's do it as though the groups were labeled:\r\n" );
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document.write( "The group of 1 is group A\r\n" );
document.write( "The first group of 2 is group B\r\n" );
document.write( "The group of 5 is group C\r\n" );
document.write( "The group of 4 is group D\r\n" );
document.write( "The second group of 2 is group E\r\n" );
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document.write( "(14C1)(13C2)(11C5)(6C4)(2C2) = (14)(78)(462)(15)(1) = 7567560\r\n" );
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document.write( "This would be the answer if the groups were labeled.\r\n" );
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document.write( "However, since they are not labeled, this number is twice too many because it\r\n" );
document.write( "considers, say,\r\n" );
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document.write( "the case where John and Mary are in group B and Sam and Lisa are in group E\r\n" );
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document.write( "as a separate case from\r\n" );
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document.write( "the case where John and Mary are in group E and Sam and Lisa are in group B.\r\n" );
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document.write( "Thus we must divide the 7567560 by 2 to eliminate all such duplications, since\r\n" );
document.write( "we are not labeling the groups.\r\n" );
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document.write( "Answer:  = 3783780\r\n" );
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document.write( "Edwin

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