## Monday, February 20, 2006

### What are the odds?

With March Madness quickly approaching, I thought this might be an appropriate question. When you fill out your bracket(s), keep in mind there are X different ways for the real outcome to occur.

What's X, assuming all outcomes are equal?

In case you aren't familiar, March Madness involves 64 (ignore the playoff for the 64th spot, please) teams. The teams are paired up in a college basketball NCAA tournament.

#### 1 comment:

1. With each matchup leading to 2 different results, and with X games in all, the number of possible outcomes is 2^X. X will be the number of teams - 1.

As a smaller example, say you had 4 teams. In the first round 2 teams face off, then the winners from the first round face each other. With three games, you would have 2^3 = 8 possible outcomes.

The number of games played in the March Madness tournament (excluding the 65 vs 64 playoff) is 63. So, the odds against you winning the march madness office pool are pretty high with 2^63 (9,223,372,036,854,775,808) possible ways for the brackets to be filled. ;-)

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