The representation of atomic configurations through cluster correlations, along with the cluster expansion approach, has long been used to predict formation energies and determine the thermodynamic stability of alloys. In this work, a comparison is conducted between the traditional cluster expansion method based on density functional theory and other potential machine learning models, including decision tree-based ensembles and multi-layer perceptron regression, to explore the alloying behavior of different elements in multi-component alloys. Specifically, these models are applied to investigate the thermodynamic stability of triple transition-metal ((Ti-Mo-V)(3)C-2 MXenes, a multi-component alloy in the largest family of 2D materials that are gaining attention for several outstanding properties. The findings reveal the triple transition-metal ground-state configurations in this system and demonstrate how the configuration of transition metal atoms (Ti, Mo, and V atoms) influences the formation energy of this alloy. Moreover, the performance of machine learning algorithms in predicting formation energies and identifying ground-state structures is thoroughly discussed from various aspects.