1. At a party, everyone shakes hands with everyone else. If 45 handshakes take place, how many people are at the party?
2. In a football league, each team plays one game against each other team in the league. If 55 games are played, how many teams are in the league?
3. A restaurant offers its customers a choice of three side dishes with each meal. The side dishes can be chosen from a list of 15 possibilities, with duplications allowed. For instance, a customer can order two sides of mashed potatoes and one side of string beans. Show that there are 680 possible options for the three side dishes.