1. The U.S. Senate consists of two senators from each of the 50 states. Five senators are to be selected at random to form a committee. What is the probability that no two members of the committee are from the same state?
2. A factory produces LCD panels, which are packaged in boxes of 10. Three panels are selected at random from each box for inspection. The box is rejected if at least one of these three panels is defective. What is the probability that a box containing six defective panels will be rejected?
3. A bag contains nine tomatoes, of which one is rotten. A sample of three tomatoes is selected at random. What is the probability that the sample contains the rotten tomato?