document.write( "Question 892503: In how many way can 12 similar balls be divided into 3 group with each group containing at most 6 balls \n" ); document.write( "
Algebra.Com's Answer #540578 by Edwin McCravy(20081)\"\" \"About 
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document.write( "If the smallest of the three groups contains\r\n" );
document.write( "only 1 ball, the other two groups must contain\r\n" );
document.write( "the other 11 balls, which can only be done with\r\n" );
document.write( "the middle sized group having 5 and the largest\r\n" );
document.write( "group having 6.\r\n" );
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document.write( "1.  The 3 groups are of sizes 1, 5,  and 6. \r\n" );
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document.write( "If the smallest of the three groups contains\r\n" );
document.write( "2 balls, the other two groups must contain\r\n" );
document.write( "the other 10 balls, which can be done two\r\n" );
document.write( "ways. The middle sized group can have 4 and the \r\n" );
document.write( "largest group has 6.  Or they can have 5 each:\r\n" );
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document.write( "2.  The 3 groups are of sizes 2, 4  and 6.\r\n" );
document.write( "3.  The 3 groups are of sizes 2, 5  and 5.\r\n" );
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document.write( "If the smallest of the three groups contains\r\n" );
document.write( "3 balls, the other two groups must contain\r\n" );
document.write( "the other 9 balls, which can be done two\r\n" );
document.write( "ways. The second group can also have 3 and the \r\n" );
document.write( "largest group 6.  Or the middle sized \r\n" );
document.write( "group can have 4 and the largest group 5.\r\n" );
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document.write( "4.  The 3 groups are of sizes 3, 3  and 6.\r\n" );
document.write( "5.  The 3 groups are of sizes 3, 4  and 5. \r\n" );
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document.write( "One more way.  They can have 4 balls each:\r\n" );
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document.write( "6. The 3 groups are of sizes 4, 4, and 4.\r\n" );
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document.write( "So there are 6 ways to divide the 12 balls into 3 groups,\r\n" );
document.write( "with no group larger than 6.\r\n" );
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document.write( "Edwin
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