It is up to the individual school membership to decide how teams will select a problem. At some schools, the coordinator assigns problems to the teams. At other schools, each team chooses the problem they prefer. Some schools mix these approaches.
If your team gets to choose the problem, one possible process would be to have the team read the synopsis for each problem on our website to see if any of the problems sparks an interest or ideas. Then read the problem statement entirely and take a vote. Remember that Problems 1 (Vehicle), 2 (Technical), and 4 (Balsa Structure) have technical requirements (that is, something has to be built) in addition to the creation of the 8-minute skit.