document.write( "Question 1173626: A five item multiple choice quiz offers 4 options (A,B,C,D) for each item. How many ways can this quiz be answered such that at least 4 items are correct. \n" ); document.write( "

Algebra.Com's Answer #798886 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A five item multiple choice quiz offers 4 options (A,B,C,D) for each item.
\n" ); document.write( "How many ways can this quiz be answered such that at least 4 items are correct.
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document.write( "\"at least 4 items are correct\" means that in four of these 5 items, the answer is PECISELY as NEEDED, in correct position.\r\n" );
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document.write( "So, there are  = 5 ways to select these correctly answered items;\r\n" );
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document.write( "and then for the single remaining item you have 4 options to answer incorrectly.\r\n" );
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document.write( "It gives  5*4 = 20  ways to have exactly 4 items answered correctly.\r\n" );
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document.write( "Add to it the case when ALL FIVE items are answered correctly, and you will get the ANSWER to the problem's question\r\n" );
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document.write( "      20 + 1 = 21.\r\n" );
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The post-solution note:

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\n" ); document.write( "\n" ); document.write( "            @ewatrrr produced different answer from mine, and it REQUIRES me to make explanations.\r
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\n" ); document.write( "\n" ); document.write( "            The cause is in that @ewatrr INCORRECTLY treats the notion \"answer\".\r
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\n" ); document.write( "\n" ); document.write( "                    In this context, the answer IS NOT HOW or WHAT the teacher evaluates the student's answer.\r
\n" ); document.write( "\n" ); document.write( "                     It is not a \"CORRECT\" or \"INCORRECT\" output value of the item.\r
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\n" ); document.write( "\n" ); document.write( "                     For each \"item\", the answer is one of options A, B, C, or D, marked by student and treated as the answer.\r
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\n" ); document.write( "\n" ); document.write( "                     It is absolutely standard and traditional interpretation in this kind of problems.\r
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\n" ); document.write( "\n" ); document.write( "            Keeping it in mind, EVERYBODY should CLEARLY UNDERSTAND that my solution is CORRECT,\r
\n" ); document.write( "\n" ); document.write( "            while @ewatrrr solution is WRONG.\r
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\n" ); document.write( "\n" ); document.write( "They are VERY ELEMENTARY conceptions for this kind of problems, that everybody knows or should know --- but not @ewatrrr.\r
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