Final answer:
There are 10! (10 factorial) different ways the students can line up.
Step-by-step explanation:
To determine the number of different ways the students can line up, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we have 10 students, so there are 10 positions available for the first student, 9 positions available for the second student, and so on. Therefore, the number of different ways the students can line up is 10! (10 factorial), which is equal to 3,628,800.