Answer:
Choose the first alternative
[tex]\displaystyle P=\frac{_{1}^{6}\textrm{C}\ _{1}^{5}\textrm{C}}{_{2}^{20}\textrm{C}}[/tex]
Step-by-step explanation:
Probabilities
The requested probability can be computed as the ratio between the number of ways to choose two sophomores in alternate positions [tex](N_s)[/tex] and the total number of possible choices [tex](N_t)[/tex], i.e.
[tex]\displaystyle P=\frac{N_s}{N_t}[/tex]
There are 6 sophomores and 14 freshmen to choose from each separate set. There are 20 students in total
We'll assume the positions of the selections are NOT significative, i.e. student A/student B is the same as student B/student A.
To choose 2 sophomores out of the 6 available, the first position has 6 elements to choose from, the second has now only 5
[tex]_{1}^{6}\textrm{C}\ _{1}^{5}\textrm{C} \text{ ways to do it}[/tex]
The total number of possible choices is
[tex]_{2}^{20}\textrm{C} \text{ ways to do it}[/tex]
The probability is then
[tex]\boxed{\displaystyle P=\frac{_{1}^{6}\textrm{C}\ _{1}^{5}\textrm{C}}{_{2}^{20}\textrm{C}}}[/tex]
Choose the first alternative
