9,223,372,036,854,775,808 possible ncaa march madness brackets
The odds of a perfect NCAA bracket are slim, 9.2+ quintillion (2^63) to one.
Of course, not all brackets are equally likely. For example, the likelihood of, say, a 16th seed beating a number 1 seed is quite low. In fact, it has never happened. So if you’re filling out a bracket, then sticking with the extant seedings might be a solid way to go. Here’s a table that shows the seed of the winners since 1985.
For more, computer scientist Sheldon Jacobson (University of Illinois) maintains a web site, Bracket Odds, with all kinds of bracketology calculators, trivia and statistics. Here’s a short piece on (pdf) “March Madness Math.”
As an aside —- schools represented by orgtheory bloggers did quite well in the tournament seeding: Duke (30-4) received a #1 seed, Notre Dame (26-6) a #2 seed, and BYU (30-4) a #3 seed.