document.write( "Question 997666: On an assignment, students are expected to answer at least 3 questions from a 16 question set. But they can complete as many questions as they wish (for bonus!). How many possible ways can they complete the assignment? \n" ); document.write( "
Algebra.Com's Answer #616072 by Edwin McCravy(20054)\"\" \"About 
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document.write( "On an assignment, students are expected to answer at least\r\n" );
document.write( "3 questions from a 16 question set. But they can complete \r\n" );
document.write( "as many questions as they wish (for bonus!). How many \r\n" );
document.write( "possible ways can they complete the assignment?\r\n" );
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document.write( "First we calculate the number of ways where they do not have \r\n" );
document.write( "to answer at least three.  Then we'll calculate the number \r\n" );
document.write( "of ways in which exactly 0, 1, or 2 are answered.  Then we'll\r\n" );
document.write( "subtract the second number from the first.\r\n" );
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document.write( "1.  We calculate the number of ways where they do not have \r\n" );
document.write( "to answer at least three, but can answer from 0 up to 16.\r\n" );
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document.write( "There are 2 choices for question 1, answer it or don't.\r\n" );
document.write( "There are 2 choices for question 2, answer it or don't.   \r\n" );
document.write( "There are 2 choices for question 3, answer it or don't.\r\n" );
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document.write( "There are 2 choices for question 15, answer it or don't.\r\n" );
document.write( "There are 2 choices for question 16, answer it or don't.\r\n" );
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document.write( "So the number of ways a student can answer any number from\r\n" );
document.write( "none at all up to all 16 is 216.\r\n" );
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document.write( "2. a. We calculate the number of ways when none are answered.\r\n" );
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document.write( "There is just one way 16C0 = 1\r\n" );
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document.write( "   b. We calculate the number of ways when only 1 is answered. \r\n" );
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document.write( "There are 16 ways, 16C1 = 16\r\n" );
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document.write( "   c. We calculate the number of ways when only 2 are answered. \r\n" );
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document.write( "There are 16C2 = 120 ways    \r\n" );
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document.write( "Answer:  216-1-16-120 = 65399\r\n" );
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document.write( "Edwin
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