difficult probability calculation

From: patrick (picogoethe_at_hotmail.com)
Date: 02/28/05 

Date: Mon, 28 Feb 2005 20:13:58 +0000 (UTC)

this problem has been haunting me for 2 weeks now. any suggestions?

given: a set of items labeled 1,...,N. at random, select a set of L
of the items and record the labels of the items contained in the set.
discard each item after it has been selected K times, otherwise
replace the items and repeat. the process terminates when there are
fewer than L items remaining.

question:
for any two items i and j, what is the probability that item i and
item j were selected together m times, m=0,...,K?

Quantcast