To find the probability of selecting a student with blue eyes, we first need to determine the total number of students.
We can calculate the total number of students by adding the number of students with each eye color:
\[ 20 , (\text{blue}) + 12 , (\text{brown}) + 10 , (\text{green}) + 8 , (\text{amber}) + 6 , (\text{hazel}) + 4 , (\text{grey}) = 60 \]
Now we know that there are a total of 60 students. The number of students with blue eyes is 20.
The probability \( P \) of selecting a student with blue eyes is given by the formula:
\[ P(\text{blue eyes}) = \frac{\text{Number of students with blue eyes}}{\text{Total number of students}} = \frac{20}{60} \]
To simplify the fraction \( \frac{20}{60} \), we can divide the numerator and the denominator by their greatest common divisor, which is 20:
\[ \frac{20 \div 20}{60 \div 20} = \frac{1}{3} \]
Thus, the chance of selecting a student with blue eyes, in the simplest form of a fraction, is:
\[ \boxed{\frac{1}{3}} \]