document.write( "Question 1208704: In how many ways can you distribute $8$ indistinguishable balls among $6$ distinguishable boxes, if at least four of the boxes must be empty? \n" ); document.write( "
Algebra.Com's Answer #847111 by Edwin McCravy(20055)\"\" \"About 
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document.write( "Case 1. 5 empty boxes.  So 1 of the 6 boxes must contain all 8 balls.\r\n" );
document.write( "That's 6 ways.\r\n" );
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document.write( "Case 2. There are 4 empty boxes, and 8 balls total in the other 2 boxes.  \r\n" );
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document.write( "Subcase 2a: The other two contain 4 balls each. there are C(6,2)=15 \r\n" );
document.write( "ways to choose 2 boxes to put them in.\r\n" );
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document.write( "Subcase 2b: The other two non-empty boxes contain 1&7, 2&6 or 3&5 balls.  \r\n" );
document.write( "For each of those three distributions, choose a box for the larger number \r\n" );
document.write( "of balls 6 ways, then a box for the smaller number of balls 5 ways. \r\n" );
document.write( "That's 3*6*5=90 ways\r\n" );
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document.write( "That's 15+90=105 for case 2\r\n" );
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document.write( "Total number of cases: 6+105=111.\r\n" );
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document.write( "Edwin
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