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 3/4…

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