document.write( "Question 1025984: if a given set has nine elements, how many of its subsets have at least five elements? \n" ); document.write( "
Algebra.Com's Answer #641316 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The first solution above is correct.  \r\n" );
document.write( "But it's not easy to see why half have 5 or more\r\n" );
document.write( "and the other half don't.\r\n" );
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document.write( "The second solution above is incorrect.\r\n" );
document.write( "She went for the subsets with fewer than 5 elements,\r\n" );
document.write( "because their complements all have 5 elements or more.\r\n" );
document.write( "That way would have been correct.  But she made a\r\n" );
document.write( "mistake and included the subsets with 5 elements, but \r\n" );
document.write( "she shouldn't have because their complements have only \r\n" );
document.write( "4 elements. \r\n" );
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document.write( "The correct and the easiest way to understand\r\n" );
document.write( "is to add the combinations of 9 elements taken\r\n" );
document.write( "5 or more.\r\n" );
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document.write( "9C5+9C6+9C7+9C8+9C9 = 126+84+36+9+1=256.\r\n" );
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document.write( "Edwin
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