In how many ways can a teacher arrange 5 students in the front row of a classroom with a total of 20 students?

In the first chair in front row, the teacher can choose from 20 students. She can choose from the remaining 19 to be seated in the 2nd chair. 18 for the 3rd chair. 17 for the 4th chair and lastly 16 for the 5th chair. The number of ways is the product of all these numbers. Thus, the teacher can arrange them in 1860480 ways.

Slot method

5 slots

1st slot: 20

2nd slot: 19 (1 went to first slot)

3rd slot: 18

4th slot: 17

5th slot: 16

20*19*18*17*16=186,040 ways