Let's break down the problem step-by-step to determine which expression represents the probability that both students chosen are sophomores.
1. Identify the basics:
- Total students: 6 sophomores + 14 freshmen = 20 students.
- Number of sophomores to be chosen: 2 sophomores.
2. Calculate the number of ways to choose 2 sophomores out of 6:
- The notation for the number of combinations (ways to choose) of 2 items from 6 is [tex]\( \binom{6}{2} \)[/tex].
- Let’s note this down for our purpose.
3. Calculate the number of ways to choose 2 students out of the total 20 students:
- The notation for the number of combinations of 2 items from 20 is [tex]\( \binom{20}{2} \)[/tex].
- We will use this in our probability calculation.
4. Form the desired probability:
- The probability that both chosen students are sophomores is the ratio of the number of favorable outcomes (2 sophomores from 6) to the number of possible outcomes (2 students from 20).
- Mathematically, this can be represented as:
[tex]\[
\text{Probability} = \frac{\binom{6}{2}}{\binom{20}{2}}
\][/tex]
Given that this expression matches the options provided, we can determine the correct choice:
[tex]\[ \boxed{\frac{{ }_6 C_2}{{ }_{20} C_2}} \][/tex]
Hence, the correct expression representing the probability that both students chosen are sophomores is:
[tex]\[ \frac{{ }_6 C_2}{{ }_{20} C_2} \][/tex]
