The probability is 0.006, or 0.6%.
This is binomial; there are a fixed number of trials (10), the events are independent (the chances of one occurring do not affect the chances of the other occurring), and there are two outcomes (either right or wrong).
He must get 6 of the 10 questions correct, so k is 6 and n is 10. The probability of getting a question correct is 1/5=0.2; the probability of getting a question incorrect is 4/5=0.8.
[tex]_{10}C_6\times(0.2)^6\times(1-0.2)^{10-6}
\\
\\\frac{10!}{6!4!}\times(0.2)^6\times(0.8)^4
\\
\\210(0.2)^6\times(0.8)^4=0.0055\approx0.006[/tex]
