1. Two out of the seven members of a school board feel that all high school students should be required to take a course in coding. A pollster selects three members of the board at random and asks them for their opinion on requiring a coding course. What is the probability that at least one of the members polled favors requiring the course?
2. Of the 15 members on a Senate committee, 10 plan to vote "yes" and 5 plan to vote "no" on an important issue. A reporter attempts to predict the outcome of the vote by questioning six of the senators. Find the probability that this sample is precisely representative of the final vote. That is, find the probability that four of the six senators questioned plan to vote "yes."
3. In the 114th United States Congress, the House Committee on Rules consisted of nine Republicans and four Democrats. If a subcommittee of three committee members was selected at random, what is the probability that at least one Democrat was on the committee?