March 27, 2017

And then there were four: South Carolina in the East bracket, Gonzaga in the West bracket, Oregon in the Midwest bracket and North Carolina in the South bracket. These four teams have earned a coveted spot in the arena known as the Final Four. There were 64 teams (not including play-in games) who entered the NCAA Tournament – 16 teams in each of the four brackets. The tournament is a single elimination, meaning each game played eliminates one team. How many games had to be played to determine the Final Four?

If each game eliminates 1 of the 64 teams, to narrow the field to 4 teams, 64 ­­– 4 = 60 teams were eliminated and 60 games were played.


Since one team from each of the four brackets of 16 teams advances to the Final Four, how many possible Final Four team combinations were possible?

For each bracket, there were 16 possible choices. Since there are four brackets, there were 16 × 16 × 16 × 16 = 164 = 65,536 possible Final Four team combinations.


Assuming equal probability of winning for each team, what is the probability that the championship game is South Carolina against North Carolina, and North Carolina then wins the national championship?  

South Carolina has a ½ chance of making it to the final. North Carolina also has a ½ chance of making the final. If this happens, there is a ½ chance that North Carolina beats South Carolina. This scenario therefore has a ½ × ½ × ½ = 1/8 probability.


Page 1 of the linked PDF contains PROBLEMS & SOLUTIONS.
Page 2