A manufacturing company in city A wishes to truck its product to 4 different cities, B,C,D, and E. If the cities are all interconnected by roads, how many different route plans can be constructed so that a single truck, starting from A, will visit each city exactly once, then return home? Solution There are four cities we have to visit before returning home, and we can do them in any order. For the first city, there are four choices. The second, three. The third, two, and the fourth only one. Multiplying 4*3*2*1 or 4! = 24 route plans total..