【Example 8】A one-way bus with a full capacity of 25 people, has a total of 14 stops along its route, and passengers can board and alight at any of the intermediate stops. Passengers traveling from different starting points to different destinations should buy different tickets. In a single trip, what is the maximum number of different tickets that can be sold on the bus?
The train should prepare tickets for each station to all the stations that come after it, so in total, it should prepare
$$
13+12+\cdots+2+1=91
$$

different types of tickets. However, it is impossible to sell all of them in a single one-way trip. Let's consider the tickets that have one of the first 7 stations as the starting point and one of the last 7 stations as the destination. There should be $7 \times 7 = 49$ such tickets. All passengers holding these tickets need to travel through the route between station 7 and station 8. However, since the train's maximum capacity is 25 people, at least $49-25=24$ of these tickets will not be sold. Therefore, the train can sell at most $91-24=67$ different types of tickets. Below, we will show that it is indeed possible to sell 67 different types of tickets:
Station 5, stations 6 to 11 each 1 person; Station 6, stations 7 to 11 each 1 person;
Station 11, stations 12 to 14 each 1 person; Station 12, stations 13 to 14 each 1 person;
Station 13, station 14 1 person.
The number of passengers on the train during each segment of the journey is: $\xrightarrow{24 \curlywedge}$ Station 10 $\xrightarrow{21 \curlywedge}$ Station 11 $\xrightarrow{16}$ Station 12 $\xrightarrow{11}$ Station 13 $\xrightarrow{6 \curlywedge}$ Station 14.