Three freshmen, five sophomores, and four juniors are on the school's chess team. the coach must select three students to attend the citywide tournament. which expression could be used to determine how many different groups of three students can be made from this team? (1) 12c3 (3) 3c1 • 5c1 • 4c1 (2) 12p3 (4) 3p1 • 5p1 • 4p1

The first expression, 12C3, is the right answer. There is no limitation saying that the team must be made up of one student from each year level. Furthermore, no distinction has been made among the three players (no assignments of Boards 1, 2, or 3), as the question just asks how many different groups. Since order does not matter, this is a combination. (If order mattered, this would be a permutation).