1. Of the nine contestants in a contest, three will receive cars, three will receive TV sets, and three will receive radios. In how many different ways can the prizes be awarded?
2. A corporation has four employees that it wants to place in high executive positions. One will become president, one will become vice president, and two will be appointed to the board of directors. In how many different ways can this be accomplished?
3. The 10 members of a city council decide to form two committees of six to study zoning ordinances and street-repair schedules, with an overlap of two committee members. In how many ways can the committees be formed?
4. In how many ways can the 14 children in a third-grade class be paired up for a trip to a museum?