# Meeting probability generalized: different wait times and number of meetings

I am looking to extend the problem of two people meeting for lunch, for example as found here:
Chance of meeting in a bar

However, I am trying to generalize this problem in two ways which, in isolation, I have found solutions to, but I have been unable to bring them together. The two generalizations are:

First, I want to extend the problem to any number of people N, and be able to find the probability that some m < N people will meet. This is covered here:
http://www.mathpages.com/home/kmath580/kmath580.htm

Second, I want to allow each individual's wait time to vary (for example person A waits for 3 minutes, person B waits 15, etc), randomly within a range. If it simplifies things, the population of wait times can be known. I have found an answer to this part here:
http://www.mathpages.com/home/kmath124/kmath124.htm
but it does not cover my first generalization.

What I'm looking to do is essentially combine those two solutions into one fully generalized probability that m of N people with random wait times will meet in a given time period.

Please let me know if anything is unclear, and thanks in advance for the help!