In order to solve this problem, you need to consider permutations.
You have 10 slots: you can assign the first slot to any of the 15 students, the second one to one of the remaining 14 students, the third slot to the remaining 13 students, and so on until the tenth slot is asseigned among the remaining 6 students. Then, you have no more slots to assign.
The total possibilities are:
15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 = 10897286400
