document.write( "Question 1207776: How many random ways can a 20-question multiple-choice test be answered, with each question having 4 options? \n" ); document.write( "

Algebra.Com's Answer #845853 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "How many random ways can a 20-question multiple-choice test be answered,
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document.write( "Imagine that the option are A, B, C, D  (i.e., the options are marked by letter A, B, C, and D).\r\n" );
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document.write( "Then one whole answer to 20 multiple choice question is a 20-letters word, written in the alphabet A, B, C, D.\r\n" );
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document.write( "Different answers create different words, and different words correspond to different answers.\r\n" );
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document.write( "So, the problem's question is the same as to ask: how many 20-letters words \r\n" );
document.write( "do exist in 4-letter alphabet A, B, C, D.\r\n" );
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document.write( "The letters in different positions are independent; in each position, any of 4 letters can be.\r\n" );
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document.write( "So, the ANSWER is:   = 1099511627776  different 20-letter words are possible \r\n" );
document.write( "in the alphabet A, B, C and D.\r\n" );
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document.write( "Hence,   = 1099511627776  different answers are possible in this multiple choice test.\r\n" );
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\n" ); document.write( "\n" ); document.write( "This model using words of the certain length written in some alphabet is useful for solving such problems
\n" ); document.write( "on multiple choice tests, and for solving many other combinatorics problems, where there is
\n" ); document.write( "a finite number of independent trials with the fixed number of independent outcomes for each trial.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) problems of this kind, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Combinatoric problems for entities other than permutations and combinations \r
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