Physically Incorrect

Level of Difficulty: Undergraduate

7 single men and 8 single women go together to see a movie. They’ve reserved in advance 15 seats. When they get to the cinema they seat themselves down randomly. What is the average number of pairs (man-woman, or woman-man) that are formed this way? For example, for the following configuration,

M M M M M M F M F F F F F F F

that number would be 3 (M stands for Male, F for Female).

Note: I’ve marked this problem as having ‘undergraduate’ difficulty since the solution I’m aware of is slightly formal (although elegant and short). If you end up with an elementary solution please share!

EDITED, 1/July/2009: a solution has been posted here.