Multi-Mode Resource Constrained Project Problem (MRCPSP) is a multi-component problem which combines two interacting sub-problems; activity scheduling and mode assignment. Multi-component problems have been of research interest to the evolutionary computation community as they are more complex to solve. Estimation of Distribution Algorithms (EDAs) generate solutions by sampling a probabilistic model that captures key features of good solutions. Often they can significantly improve search efficiency and solution quality. Previous research has shown that the mode assignment sub-problem can be more effectively solved with an EDA. Also, a competitive Random Key based EDA (RK-EDA) for permutation problems has recently been proposed. In this paper, activity and mode solutions are respectively generated using the RK-EDA and an integer based EDA. This approach is competitive with leading approaches of solving the MRCPSP.