For many data analysis tasks, obtaining the causal relationships between interacting objects is of crucial interest. Here, the case of modelling causal relationships via causal orderings is considered. Triplet ordering preferences are used to perform Monte Carlo sampling of the posterior causal orderings originating from the analysis of experiments involving observation as well as, usually few, interventions, like knockouts in case of gene expression. The performance of this sampling approach is compared to a previously used sampling via pairwise ordering preference as well as to the sampling of the full posterior distribution. This is performed for artificially generated causal, i.e. directed acyclic graphs (DAGs) with a scale-free structure, i.e. a power-law distribution for the out-degree. The sampling using the triplets ordering turns out to be superior to both other approaches, similar to our previous work, where the less-realistic case of Erdős-R nyi random graphs was considered.