document.write( "Question 840075: student has 6 questions. student can score 0, 1, 2, or 3 per question. how many ways can student get 15? \n" ); document.write( "

Algebra.Com's Answer #506175 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "There must be at least 3 questions with scores of 3, for if there\r\n" );
document.write( "were only 2 with scores of 3, that would be only be 6, leaving the\r\n" );
document.write( "other 15-6 or 9 to be made with 3 scores of 2 or less, which is\r\n" );
document.write( "impossible.  \r\n" );
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document.write( "So the 3 scores of 3 each accounts for 9, so the other 15-9 or 6,\r\n" );
document.write( "must be made with 3 questions.  The only ways to get 6 with\r\n" );
document.write( "3 questions is 0+3+3, 1+2+3, or 2+2+2.\r\n" );
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document.write( "0+3+3+3+3+3 = 15\r\n" );
document.write( "1+2+3+3+3+3 = 15\r\n" );
document.write( "2+2+2+3+3+3 = 15\r\n" );
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document.write( "So there are only 3 basic ways to get 15.  However we must permute these\r\n" );
document.write( "over all 6 questions.\r\n" );
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document.write( "The number of distinct permutations of 0,3,3,3,3,3 is \r\n" );
document.write( "The number of distinct permutations of 1,2,3,3,3,3 is \r\n" );
document.write( "The number of distinct permutations of 2,2,2,3,3,3 is \r\n" );
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document.write( "Answer: 6+30+20 = 56 ways possible to get 15  \r\n" );
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document.write( "Edwin

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