document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210229>Question 1210229</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the number of subsets of<BR>\n" );
document.write( "S = \{1, 3, 8, 17, 30, 36, 47, 58\},<BR>\n" );
document.write( "so that the sum of the elements in the subset is less than 20. (Note that for the empty subset, we take the sum of the elements as 0.)<BR>\n" );
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document.write( "Since the elements 30, 36, 47, and 58 are each alone greater than 20, the only elements we need to consider are 1, 3, 8, and 17.<br><BR>\n" );
document.write( "subsets with 0 elements: { }<BR>\n" );
document.write( "Number of subsets with 0 elements and a sum of less than 20: 1<br><BR>\n" );
document.write( "subsets with 1 element: {1}, {3}, {8}, {17}<BR>\n" );
document.write( "Number of subsets with 1 element and a sum of less than 20: 4<br><BR>\n" );
document.write( "subsets with 2 elements: {1,3}, {1,8}, {1,17}; {3,8}<BR>\n" );
document.write( "Number of subsets with 2 elements and a sum of less than 20: 4<br><BR>\n" );
document.write( "subsets with 3 elements: {1,3,8}<BR>\n" );
document.write( "Number of subsets with 3 elements and a sum of less than 20: 1<br><BR>\n" );
document.write( "Total number of subsets with a sum of less than 20: 1+4+4+1 = 10<br><BR>\n" );
document.write( "ANSWER: 10<br><BR>\n" );
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