How hard it is to pick the perfect bracket?

Games have begun and there have been several upsets but March Madness won't be over until the finals on April 3rd and 4th. March Madness bracket predictions can still be reworked.

This year there will are 68 men's and 64 women's college basketball teams in the tournaments.

If you try to predict how the games will play out by filling out a bracket, what are your chances of picking every game? How does the change from 64 to 65 to now, 68 teams in the field complicate things?  How many brackets would you need to fill out to pick every possibility?  How many reams of paper would you need to print all of those brackets?  Let’s do the math!   Also, check out the video below that explores your odds of picking all games in the tournament perfectly.

For Adventurer members we have an editable Word docx and solutions.

Note: The last problem in this activity asks students to determine how a math professor came up with a particular probability.  We are not sure how the professor came up with 1/128 billion, we give a few possibilities in the solutions.  The main point of that question is to promote some creative thinking and discussion while students grapple with ways to reach 1/128 billion.

Thanks to Matt Timmins, Newton teacher, for creating the draft of this post.