Question: Suppose you were given an n-question multiple-choice examination in which each question had 5 possible answers. Assume that you were forced to purely guess for each question.

1. Let n = 20. Suppose it takes at least one-third of the 20 questions correctly to pass the test. What is the exact probability of passing?
2. Let n = 8. Suppose through some studying you are able to correctly eliminate 3 answers on each question. What is the exact probability of making a perfect score?

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