For embedded unitary ensembles with SU(Ω) × SU(r) embedding and generated by random two-body (in some situations k-body) interactions preserving SU(r) symmetry, analytical formulas, in terms of SU(Ω) Racah coefficients, are derived for the lower order moments of the one and two-point functions in eigenvalues. This formulation unifies all known results and new results are derived for r = 3. Similarly, the method of binary correlation approximation developed for spinless identical fermion systems, has been extended to proton-neutron systems and it is used to show that the bivariate transition strength density appropriate for neutrinoless double beta decay will be close to a bivariate Gaussian. In addition, trace propagation methods of French are also used to derive analytical results for embedded ensembles and they have opened a new window to understand regular structures generated by random interactions.