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. © 2010 IOP Publishing Ltd.