  Urn models play an important role to express various basic ideas in
probability theory. Here we extend this urn model with tubes. An urn contains
coloured balls, which can be drawn with probabilities proportional to the
numbers of balls of each colour. For each colour a tube is assumed. These tubes
have different sizes (lengths). The idea is that after drawing a ball from the
urn it is dropped in the urn of the corresponding colour. We consider two
associated probability distributions. The first-full distribution on colours
gives for each colour the probability that the corresponding tube is full
first, before any of the other tubes. The negative distribution on natural
numbers captures for a number k the probability that all tubes are full for the
first time after k draws.
  This paper uses multisets to systematically describe these first-full and
negative distributions in the urns & tubes setting, in fully multivariate form,
for all three standard drawing modes (multinomial, hypergeometric, and Polya).
