1. Suppose that the sportswriter in Exercise 36 simply puts the 12 team names in a hat and draws 3 completely at random. Does this increase or decrease the writer's chance of picking at least one winner?
2. Fred has five place settings consisting of a dinner plate, a salad plate, and a bowl. Each setting is a different color. If Fred randomly selects a dinner plate, a salad plate, and a bowl, what is the probability that they will all have different colors?
3. Michael and Christopher are among seven contestants in a race to be run on a seven-lane track. If the runners are assigned to the lanes at random, what is the probability that Michael will be assigned to the inside lane and Christopher will be assigned to the outside lane?