document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207776>Question 1207776</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many random ways can a 20-question multiple-choice test be answered, with each question having 4 options? </SPAN>\n" );
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document.write( "Answer: <font color=red>1,099,511,627,776</font><BR>\n" );
document.write( "This is roughly 1.0995 trillion\r<BR>\n" );
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document.write( "Work Shown<BR>\n" );
document.write( "4^20 = 1099511627776\r<BR>\n" );
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document.write( "Explanation<BR>\n" );
document.write( "Let's say for the sake of simplicity there are 2 questions with 4 options each.<BR>\n" );
document.write( "Consider a 4 by 4 table. There are 4*4 = 4^2 = 16 different ways to answer these two questions. <BR>\n" );
document.write( "This is because there are 16 inner cells of this table.\r<BR>\n" );
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document.write( "Now consider a test with 3 questions. Each has 4 options.<BR>\n" );
document.write( "We found earlier that there are 16 ways to answer the first two questions. <BR>\n" );
document.write( "Consider a table that has 16 rows and 4 columns. <BR>\n" );
document.write( "The row count is how many ways to answer the first two questions, while the columns are the options for the third question.<BR>\n" );
document.write( "We have 16*4 = 64 ways to answer these 3 questions<BR>\n" );
document.write( "Or put another way 4^3 = 64<BR>\n" );
document.write( "This pattern can be continued for as long as you like.\r<BR>\n" );
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document.write( "In general, if an exam has n questions with 4 options each, then there will be 4^n different ways to select the options.<BR>\n" );
document.write( "In the \"work shown\" section above, I plugged in the value n = 20. <BR>\n" );
document.write( "The massive number 1099511627776 is roughly 1.0995 trillion.<BR>\n" );
document.write( "In scientific notation, it's roughly equal to 1.0995 * 10^12<BR>\n" );
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