Based on a reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm which was developed by Fronk and Giudici (2000) to deal with model selection for Gaussian dags, we propose a new approach for the pure discrete case. Here, the main idea is to introduce latent variables which then allow to fall back on the already treated continuous case. This makes it also straightforward to tackle the mixed case, i.e. to deal simultaneously with continuous and discrete variables. The performance of the approach is investigated by means of a simulation study for different standard situations. In addition, a real data application is provided.