Question: Let's generalize Problem to a regional Ultimate Frisbee tournament where there are n teams attending. Teams are assigned numbers (1 through n) when they register. As before, each team will play each other exactly once.
(a) How many games does Team 1 play?
(b) How many games does Team 2 play? Wait, that counts the Team 1 versus Team 2 game twice. How many not-yet-counted games does Team 2 play?
(c) Keep going. How many "new" (uncounted) games does Team i play?
(d) How many games are played in total?
Problem: Some conference-goers saunter over to the Healthy Snack Box Machine, where they each choose one of five kinds of fruit, one of three herbal teas, and one of six flavors of wrap sandwich to get packed in a box. How many possible snack boxes are there?