Traveling from A to B gives 4 options, from B to C gives 5 options, and from C to A gives 6 options. This yields. 4 × 5 × 6 = 120 paths from A to B to C to A. However, a round trip could start at A or B or C. Hence, there are 3 different starting/ending points. This gives us 3 × 120 = 360 paths. However, a round trip starting and ending at A could be A to B to C to A or A to C to B to A. Hence, there are two directions of travel, giving 2 × 360 = 720 paths.