Answer: 4,080.
Step-by-step explanation:
Since the teacher has 17 students and they need to assign three different roles each day (line leader, door holder, and materials handler) To find how many ways she can fill these roles, we can use the concept of permutations.
Since we want to find the number of ways to arrange 17 students into three different positions, we can start by considering the line leader position. Since there are 17 students, any one of them can be the line leader, leaving 16 students to be available for the door holder position, any one of those 16 students can be the door holder, leaving 15 students left for the materials handler.
Now, to find the total number of ways to fill all three of these roles, we multiply the number of choices for each position together, 17x16x15=4,080
Meaning, the Teacher can fill the roles of line leader, door holder, and materials handler in 4,080 different ways with her 17 students each day.
Now I'm not saying this is realistic, but this is the answer.