There are 8 sprinters in the Olympic 100-meter finals.  The gold medal goes to first place, silver to second, and bronze to third.   In how many ways can the medals be awarded?
I need to count the number of possible outcomes for the medal positions. For the gold medal, there are 8 possible sprinters who could win it. For the silver medal, there are 7 possible sprinters left, since one of them already won the gold. For the bronze medal, there are 6 possible sprinters left, since two of them already won the gold and silver. So the total number of outcomes is the product of these numbers: 8 x 7 x 6. I can use a calculator or do this mentally: 8 x 7 = 56, and 56 x 6 = 336. So there are 336 ways to award the medals. 