Cluster analysis is a powerful, versatile tool used in several fields to classify objects according to a set of observed characteristics. This analysis commonly involves some critical decisions, such as choosing the number of clusters to consider. To help practitioners undertake this specific challenge, we propose a permutation-based approach which makes it possible to compute a ranking of $C$ different partitions into $K_c$, $c=1,\ldots,C$ clusters. In particular, this procedure avoids choosing a single clustering quality index for the choice of optimal number of clusters, and bases the decision on multiple indices. A case study presenting an example of successful application of the aforementioned approach is considered.