document.write( "Question 1160018: If three people roll a dice once, how many ways can the sum of the three people’s rolls add up to exactly 9? \n" ); document.write( "

Algebra.Com's Answer #783172 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "In other form, the question is\r\n" );
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document.write( "    How many solutions does this equation have\r\n" );
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document.write( "         +  +  = 9\r\n" );
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document.write( "    in positive integer numbers ,  and  ?\r\n" );
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document.write( "The solution can be done using the \"Stars and Bars method\", which gives in this case the answer  \r\n" );
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document.write( "          =  =  = 4*7 = 28.\r\n" );
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document.write( "ANSWER.  28 different solutions   //  (accounting for all possible permutations, cases and sub-cases . . . )\r\n" );
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\n" ); document.write( "\n" ); document.write( "For the \"Stars and Bars method\", see the lesson\r
\n" ); document.write( "\n" ); document.write( " - Stars and bars method for Combinatorics problems \r
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\n" ); document.write( "\n" ); document.write( "or, alternatively, this Wikipedia article\r
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\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29\r
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\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29\r
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