Question 88730: A test has 10 true/false questions. How many different tests can be turned in to the teacher? Found 2 solutions by jim_thompson5910, bucky:Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! The first question could be answered either true or false.
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If you answered true on the first question, you could answer either true or false on the
second question.
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If you answered false on the first question you could answer either true or false on the
second question.
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So after two questions you have four possible situations:
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True & then True
True & then False
False & then True
False & then False
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Now for each of those 4 possibilities, you could answer either true or false on the third question.
So after 3 questions you would have 8 possible test answers ... 4 * 2.
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And for each of the 8 possible answer situations on the third question, you can answer either
true or false on the fourth question. This will give you 8 * 2 = 16 possible answers after
the fourth question.
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By now you have probably noticed the pattern. Each additional question increases the number
of possible answer configurations by a factor of 2.
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This pattern is reflected by the equation:
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Number of different tests = 2^n
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where n represents the number of questions on the test.
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If there were just 1 question on the test there would be 2^1 possible answers (either true
or false). If there were 2 questions on the test, the number of possible answer combinations
would be 2^2 or 4. Similarly for 3 questions there would be 2^3 = 8 possible combinations.
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Extending on this pattern, for a 10 question test there would be 2^10 possible combinations
of answers. And 2^10 = 1024 possible answer combinations. That means that the teacher
could possibly receive 1024 tests that are all different by at least one answer.
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Hope this provides you with a way of figuring out a process for solving questions
such as this one.
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