Math Quiz: NYT Learning Network

Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network.  My latest contribution, a Test Yourself quiz-question, can be found here:

https://learning.blogs.nytimes.com/2012/08/06/test-yourself-math-aug-6-2012/

This question is based on the rare tie that occurred in a Olympic qualifying race.  In how many different ways could eight racers finish first, second, and third?