document.write( "Question 1115937: A test has 6 multiple choice questions each having 4 possible answers. In how many ways can a student respond to the questions if:\r
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Algebra.Com's Answer #730774 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "a)  All questions must be answered?    <<<---=== Answer.   ways.\r\n" );
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document.write( "       Solution\r\n" );
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document.write( "    For simplicity, let us assume that you write one of the 4 letters A, B, C or D as the possible answer to each question.\r\n" );
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document.write( "    Then you have 4 opportunities for each of 6 question, which gives the above answer.\r\n" );
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document.write( "    Memorize: the space of events in this case is the space of all 6-letter words written in 4-letter alphabet.\r\n" );
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document.write( "b)  Not all questions must be answered?       <<<---=== Answer.  .\r\n" );
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document.write( "       Solution\r\n" );
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document.write( "    We can very easily reduce this problem to the previous scheme by making an agreement that we write the fifth symbol/letter  \"E\"  \r\n" );
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document.write( "    where the question is unanswered.\r\n" );
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document.write( "    Then the space of events is the space of all 6-letter words written in 5-letter alphabet, which gives the above answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The space (the set) of n-symbol words over the m-symbol alphabet is the third entity widely used in Combinatorics after Permutations and Combinations.\r
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