How many different three-person relay teams can be chosen from six students?

The first person can be any one of 6.
                 For each of those . . .
The second person can be any one of the remaining 5.
                 For each of those . . .
The third person can be any one of the remaining 4.

 Total number of ways to pick 3 people out of 6 = (6 x 5 x 4) = 120 ways.

BUT . . .

For each 3-person team, there are (3 x 2 x 1) = 6 ways to pick
the same three people.

In the 120 ways to pick 3 people, you'll find each different
group of 3 people picked 6 times, in a different order.

The number of different 3-person teams is

                         120 / 6  =  20 teams .