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A student randomly guesses each answer to a quiz consisting of 8 Yes/No questions. In how many different ways can he answer the 8 questions if he writes down more Yeses than Nos?
(Answer = 93)
I figured there were 3 scenarios. Yes = No, Yes > No and Yes < No. I also figured that Yes > No = Yes < No, as they are interchangeable. So:
For the scenario Yes = No, there are 70 different ways of answering:
Am I right so far? Help please.
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Everything so far is right, and in fact, you've already done most of the work.
In total, there are 2^8 = 256 ways of answering all of the questions, because there are 2 ways of answering each question and 8 questions.
Your reasoning about Yes>No = No>Yes was correct, so we can put that into the formula you made.
Total number of Yes>No ways: (256-70)/2 = 186/2 = 93.
Why did the vector cross the road?
It wanted to be normal.
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Pretty good problem.
Let the n be the number of the questions.
In general we'll have two cases:
1. If n is odd, then we can't have (YES=NO) case. So in this case, the answer is 2^(n-1).
2. If n is even, we'll have for the number of (YES=NO) cases:
Last edited by krassi_holmz (2006-12-24 06:21:30)
IPBLE: Increasing Performance By Lowering Expectations.
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