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Carrier gases are used in most nucleation experiments for releasing the latent heat generated during vapor condensation. In the analysis of experimental data it is often assumed that the carrier gas is inert and would not participate in the nucleation process of the target gas. Several recent nucleation experiments show that the influence of carrier gases to nucleation rate is not negligible under certain conditions. To gain more insight into the carrier-gas effect, we carry out Monte Carlo simulation to compute the free energy of formation of water clusters in the presence of a nitrogen carrier gas. At fixed temperature (240 K) and chemical potential, it is found that the barrier height to nucleation increases with the carrier-gas pressure. This barrier enhancement is attributed to the increase of equilibrium vapor pressure of water in the presence of carrier gas, which results in a decrease of supersaturation. It is also found that the simulation results are consistent with the binary-nucleation theorem.