BACKGROUND: It's time again for "March Madness," when U.S. college basketball teams compete to win the NCAA Division I Basketball Tournament, and buddies compete with each other by picking winning teams to guess the ultimate outcome of the tournament. But the realities of mathematical probability dictate that it's almost impossible to get your picks 100 percent right.
CALCULATING THE ODDS: Since there are 64 games in the March Madness tournament and two possible outcomes for each team's game -- a win and a loss -- the number of possible outcomes for the tournament is a staggering 2 to the power of 64: that is, 2 multiplied by itself 64 times, or 18,446,744,073,709,551,616. If one dollar bill represents each of the possibilities, and the six-inch bills are placed lengthwise end-to-end, the line would make two round trips between the Earth and the middle of the Big Dipper -- a distance of about 75 light years. In fact, if you put in a dollar for each of the possible ways to fill out the team bracket chart (see link below), you would be able to pay off the U.S. National Debt (about $8 trillion as of March 2004) 2.3 million times over.
THE MATH OF FILLING OUT THE POOL FORMS: Combinatorics is a mathematical theory of counting individual objects, particularly units of a finite set, like a collection of marbles stored in a small pouch. Once primarily a mathematical curiosity, it is vital to many areas of modern technology. For example, it is a useful tool in determining probabilities and the number of structures possessing certain properties as applied to telephone (fiber optic) networks and computers. It can also be used to analyze industrial process schedules, electrical networks, and economics. And it's the math that you'd use if you actually filled out every possible form.