A case study of applying the generalised K-means algorithm with different p values is provided to discuss the applicants' selection under a variety of criteria in an admission process. The properties of the generalised K-means algorithm are exploited in a decision-making process. When p is smaller and closer to zero, the results show the priorities are identical, which is to look for the applicants with even performance. In contrast, the most commonly used p values in K-means algorithm do not generate a systematic pattern. When p becomes larger and approaches ∞, the results show the priorities are difficult to tell, but the intention is to separate alternatives with a number of clusters, which is to look for the applicants with the greatest potential. Finally, in this case study, using smaller p values might provide stable priorities to select 21 applicants out of 36 participants.