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 probability that the student guesses the answers of exactly \( 8 \) questions correctly out of \( 10 \) is \( \frac{27k}{4^{10}} \), then \( k \) is equal to ________ .
