Divide the corridor into segments. Each segment has two seats, starts precisely with one seat, and ends precisely with the other seat.

How many dividers can you install between two adjacent segments? You must install precisely one. Otherwise, you would have created a section with not exactly two seats.

If there are k plants between two adjacent segments, there are k + 1 positions (ways) you could install the divider you must install.

The problem now becomes: Find the product of all possible positions between every two adjacent segments.