  We consider the conductance distributions in chaotic mesoscopic cavities for
all three invariant classes of random matrices for the arbitrary number of
channels N1, N2 in the connecting leads. We show that the Laplace transforms of
the distributions can be expressed in terms of determinants in the unitary case
and Pfaffians in the orthogonal and symplectic cases. The inverse Laplace
transforms then give the exact distributions. This formalism is particularly
useful for small values of N = min (N1, N2), and thus is of direct experimental
relevance. We also obtain the conductance distributions for orthogonal-unitary
and symplectic-unitary crossover ensembles.
