document.write( "Question 688573: The sum of the digits of the four-digit number 3527 is 17, because 3 + 5 + 2 + 7 = 17. In how many four-digit numbers is the sum of the digits equal to 34? \n" ); document.write( "
Algebra.Com's Answer #425647 by Edwin McCravy(20065)\"\" \"About 
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document.write( "The largest 4-digit mumber is 9999, which has sum of digits 9+9+9+9 = 36,\r\n" );
document.write( "so to have a sum of digits 34, we have to take 2 away.  There are 2 ways \r\n" );
document.write( "to do that:\r\n" );
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document.write( "1.  Take 2 away from 1 of the 9's and the set of digits is {7,9,9,9}.\r\n" );
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document.write( "2.  Take 1 away from 2 of the 9's and the set of digits is {8,8,9,9}.\r\n" );
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document.write( "There are 4 arrangements of the digits {7,9,9,9} because there are four \r\n" );
document.write( "positions for digits: thousands, hundreds, tens, and units. So we can pick \r\n" );
document.write( "a position for the 7 in C(4,1) = 4 ways.  [They are 7999,9799, 9979, and 9997.\r\n" );
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document.write( "There are 6 arrangements of the digits {8,8,9,9} because there are four \r\n" );
document.write( "positions for digits: thousands, hundreds, tens, and units. So we can pick \r\n" );
document.write( "a position for the 2 8's in C(4,2) = 6 ways.  [They are 8899,8989, 8998,\r\n" );
document.write( "9889, 9898 and 9988.\r\n" );
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document.write( "So that's 4+6 or 10 ways.\r\n" );
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document.write( "Edwin
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