Complete Set

Hi,
I'm a computer science student working on my final year project. My
project is dealing in depth with the bit torrent network and attempting to
localise the network and ultimately, to reduce traffic the file transfers
create on the internet.

If i have n amount of people each with a known amount of files, and knowing
that each person has no duplicate files. Is it
possible to work out the probability that collectivally they have all the files?

I have worked out a formula which works for 2 people but I need to expand
on this to n amount of people.

k = 100%
(x1 choose k-x2) (k choose x1)/ (k choose x2) (k choose x1)
(x1 choose k-x2) / (k choose x2)

Any help would gladly be appreciated
Cheers
Chris