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Considering the huge computational resources required by smoothed particlehydrodynamics (SPH) simulations and the overestimation of post-collisionmaterials from perfect merging, we develop a statistical method to deal withcollisions during the formation of planetary systems by introducing randommaterial loss. In this method the mass and water content lost by the soleoutcome from every merger vary randomly within a range dependent on the totalmass and water content of colliding bodies. The application of the random lossmethod to the planet formation in the solar system shows a good consistencywith existing SPH results. We also apply this method to the extrasolarplanetary system 55 Cancri which hosts (at least) five planets and study theformation of terrestrial planets between the outermost two planets. A disk with500 Mars mass embryos in dynamically cold orbits before the late-stageaccretion phase is assumed. Scenarios with different amounts of planetaryembryos and different loss parameters are adopted in our simulations. Thestatistical result from hundreds of simulations shows that an Earth-like planetwith water inventory of roughly 6 Earth ocean could form between 55 Cnc f andd. It may reside between 1.0 and 2.6 AU but the most likely region extends from1.5 to 2.1 AU. Thus the probability of this planet being in the potentiallyhabitable zone (0.59--1.43 AU) is relatively low, only around 10\%. Planets 55Cnc f and d could also be shaped and gain some water from giant impacts andconsequently the orbits of them may also change accordingly.

On the formation of terrestrial planets between two massive planets: The case of 55 Cancri