Let's say I have some number of individuals who are single, $(b_1, ..., b_N) \in B$, and for every possible pairing of two individuals, $b_i$ and $b_j$, I happen to know the exact probability that the two will irreversibly become married if they happen to meet. With this in mind, I select $k$ of the individuals in $B$ for a dating party, where each person randomly meets with others until all $k$ individuals are married (assuming that there are an even number of participants and only non-zero probabilities for marriage).
Knowing the probabilities that each potential couple become married, and assuming that pairings at the dating party are truly random, how do I optimally select the $k$ individuals to maximize the probability that the same pairings occur over multiple independent trials? How might I calculate the probability that one or a set of couplings occur in each trial?
Note: Strictly for the sake of this problem, pairings may occur between any two individuals without regard to gender.