The probability that a student does not have blue eyes is given by:

\(P( ext{not blue eyes}) = 1 - \frac{1}{5} = \frac{4}{5} = 0.8\)

For n students, the probability that none of them has blue eyes is:

\((0.8)^n\)

We need this probability to be less than 0.001:

\((0.8)^n < 0.001\)

Taking logarithms on both sides:

\(n \log(0.8) < \log(0.001)\)

Solving for n:

\(n > \frac{\log(0.001)}{\log(0.8)}\)

Calculating the values:

\(n > \frac{-3}{-0.09691} \approx 30.9\)

Since n must be an integer, the least possible value of n is 31.