Answer:
There are 79,800 ways in which this is possible.
Step-by-step explanation:
The order in which the students are chosen is important(due to different roles), which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
2 sophomores from a set of 20.
2 freshmen from a set of 15. So
[tex]P_{20,2}*P_{15,2} = \frac{20!}{18!}*\frac{15!}{13!} = 20*19*15*14 = 79800[/tex]
There are 79,800 ways in which this is possible.
