Blood is a multicomponent mixture comprised mostly of red-blood-cells (RBCs) along with trace amounts of other components like leukocytes, platelets, and circulating tumor cells (in the case of cancer). Under physiological flow conditions both the leukocytes and the platelets segregate near the walls of the blood vessel, a phenomenon commonly known as margination, while the RBCs tend to migrate away from the walls. The key physical differences between RBCs, leukocytes, and platelets are their relative size and rigidity: the leukocytes are larger than RBCs, while the platelets are smaller; both are considerably stiffer than RBCs. However, how these differences in properties lead to the observed segregation behavior is poorly understood. In this work we focus on a model system consisting of a fluid-filled elastic capsule mixture in which individual components differ in size and rigidity. Using detailed boundary integral simulations we delineate the effect of both of these key properties on the flow induced segregation behavior and relate these to the observations of leukocyte and platelet margination in blood flow. To gain a mechanistic understanding of these results, we introduce a master equation description of the particle dynamics that incorporates the two main ingredients of flow dynamics in confined suspensions: wall-induced migration and hydrodynamic pair collisions. We also introduce a novel hydrodynamic-Monte Carlo simulation technique for sampling this equation. The results for this model system clarify the important and previously underappreciated role played by heterogeneous collisions, i.e. collisions between two different species in a mixture, in the observed segregation behavior. The model is also shown to reproduce the results of the detailed boundary integral simulations, while requiring only a fraction of the latter's computational cost. The insights and tools presented in here will be helpful, e.g., in designing drug delivery particles for optimal vascular targeting and for designing microfluidic devices for separating/enriching trace components of blood.