In an examination, there are 10 true-false type questions. Out of 10 , a student can guess the a...

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In an examination, there are 10 true-false type questions. Out of 10 , a student can guess the answer of 4 questions correctly with probability \( \frac{3}{4} \) and the remaining 6 questions correctly with probability \( \frac{1}{4} \). If the probility that the student guesses the answers of exactly 8 questions correctly out of 10 is \( \frac{27 k}{4^{10}} \), then \( k \) is equal to
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