There are 8 sprinters in the Olympic 100-meter finals, but 2 of them are disqualified. The gold medal goes to first place, silver to second, and bronze to third. In how many ways can the medals be awarded?

If 2 are disqualified, then the remaining 6 have:

6 ways for 1st place

5 ways for 2nd place

4 ways for the 3rd place

So: There are: 6 x 5 x 4 ==120 ways that the 3 medals can be awarded.