document.write( "Question 935766: number of ways in which an examiner can assign 50 marks to 10 question giving not less than 3 marks to any question \n" ); document.write( "
Algebra.Com's Answer #572524 by Edwin McCravy(20081)\"\" \"About 
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document.write( "Let us begin by assigning 3 marks to each of the 10 questions, so that each will\r\n" );
document.write( "have at least 3 marks.\r\n" );
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document.write( "We have now assigned 30 of the 50 marks.  We have 20 more marks left to assign\r\n" );
document.write( "to questions.\r\n" );
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document.write( "Get 20+10 or 30 slips of paper. (You don't have to actually get 30 slips of\r\n" );
document.write( "paper.  You can just imagine them, but I'll talk as though you actually have\r\n" );
document.write( "30 slips of papers laid out in a row left to right). \r\n" );
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document.write( "Write the word \"Divider #10\" on the right-most slip of paper.\r\n" );
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document.write( "Now choose 9 other slips of paper from the other 29.  You can choose them\r\n" );
document.write( "C(29,9) ways. \r\n" );
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document.write( "Write \"Divider #1\" on the left-most one you chose. After Divider #1, going left\r\n" );
document.write( "to right, write \"Divider #2\" on the next one chosen on the right, and so on\r\n" );
document.write( "until the last slip chosen as a divider before Divider #10 will have \"Divider\r\n" );
document.write( "#9\" written on it.\r\n" );
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document.write( "So now we have a row of 30 slips of paper. 10 of the slips of paper, including\r\n" );
document.write( "the very last one, (the rightmost one), have \"Divider #(something)\" written on\r\n" );
document.write( "them. And 20 slips of paper have nothing written on them.\r\n" );
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document.write( "Now going left to right, count the number of slips of paper that have nothing\r\n" );
document.write( "written on them which are left of Divider #1, which may be anything from none at\r\n" );
document.write( "all (zero) through 20. Whatever that number is, assign that number of extra\r\n" );
document.write( "marks to question #1, (in addition to the 3 that have already been assigned to\r\n" );
document.write( "it.\r\n" );
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document.write( "Next count the slips of paper between dividers #1 and #2, and assign that number\r\n" );
document.write( "of marks to question 2.  \r\n" );
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document.write( "Continue doing this until all 20 marks have been assigned.\r\n" );
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document.write( "[Remember that if dividers #n and #n+1 are next to each other, then you don't\r\n" );
document.write( "assign any additional marks to question n+1.]   \r\n" );
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document.write( "The number of ways we can pick the 9 slips of paper to be dividers (besides\r\n" );
document.write( "divider #10 on the far right end) is C(29,9) = 10015005.\r\n" );
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document.write( "Answer: 10015005\r\n" );
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document.write( "Edwin
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