  In this paper we complete the derivations of finite volume partition
functions for QCD using random matrix theories by calculating the effective
low-energy partition function for three-dimensional QCD in the adjoint
representation from a random matrix theory with the same global symmetries. As
expected, this case corresponds to Dyson index $\beta =4$, that is, the Dirac
operator can be written in terms of real quaternions. After discussing the
issue of defining Majorana fermions in Euclidean space, the actual matrix model
calculation turns out to be simple. We find that the symmetry breaking pattern
is $O(2N_f) \to O(N_f) \times O(N_f)$, as expected from the correspondence
between symmetric (super)spaces and random matrix universality classes found by
Zirnbauer. We also derive the first Leutwyler--Smilga sum rule.
