First notice that the 64 teams play 63 total games: 32 games in the
first round, 16 in the second round, 8 in the 3rd round, 4 in the
regional finals, 2 in the final four, and then the national
championship game.

32+16+8+4+2+1= 63

Now let's answer an easier question.

If there were four teams, and they played three games, how many
different ways would there be to fill out a bracket?  You can write
them down. There are only eight of them. Where do that eight come
from?  Well, there are three games, and you have two possible choices
for each game. Hence, 2^3 = 8 possibilities.

Now back to the real tournament. Since there are 63 games to be
played, and you have two choices at each stage in your bracket, there
are 2^63 different ways to fill out the bracket.

2^63 = 9,223,372,036,854,775,808

That's more than nine quintillion possibilities.

Perhaps now you can see why CNNSI is so willing to give away ten
million dollars to the person that fills out a perfect bracket. It's
just not likely to happen.

Even if every person in America filled one out (300 million people),
the probability of someone winning is:

300,000,000
----------- = .00000000003253
  2^63

I don't think anyone is going to fill out a perfect bracket any time
soon.