Question

Seven athletes participate in a 100-meter sprint event. How many possible finishes are there for the first 3 positions?

Answer 1

210

Explanation:

Since this is a race, it's assumed that the finishing order is important. When ordering matters while making selections, you use permutations.

In this case, we need to select 3 positions from 7 athletes. This is defined as `""_7 P_3`, or more simply 765 = 210. This is because for 1st place there are 7 possible winners; once the first person finishes the race, there are 6 remaining athletes for 2nd place, leaving 5 for 3rd place after that.