Each year, 64 college basketball teams compete in the NCAA tournament. Sandbox.com recently offered a prize of $10 million to anyone who could correctly pick the winner in each of the tournament games. (The president of that company also promised that, in addition to the cash prize, he would eat a bucket of worms. Yuck.)

a. How many games are required to get one championship team from the field of 64 teams?

b. If someone makes random guesses for each game of the tournament, find the probability of picking the winner in each game.

c. In an article about the $10 million prize, the New York Times wrote that “even a college basketball expert who can pick games at a 70 percent clip has a 1 in __________ chance of getting all the games right.” Fill in the blank.