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If there are only a handful of objects, then you can count them with a moment's thought, but the techniques of combinatorics can extend to quickly and efficiently tabulating astronomical quantities. See more

Adam, Billy, Cathy, and David are in a race. We know that

- the fastest of them finished in 10 minutes
- the slowest of them finished in 30 minutes
- David beat Adam to the finish line by 11 minutes
- Cathy beat Billy by 13 minutes
- David was the fastest

At the end, their names are written on the scoreboard in the order in which they finished the race, from first place to last place. In how many different ways could their names be arranged?

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