Discrete Mathematics
# Discrete Mathematics Warmups

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?

You have three colors of paint, and you want to paint all sides of a regular tetrahedron (a polyhedron with 4 equilateral triangles faces).

How many ways are there to do so if you only paint each face one of your three colors? (Rotations of the tetrahedron are considered equivalent).