Mixing and fallback models in faint supernova models are supposed to reproduce the abundance patterns of observed carbon-enhanced metal-poor (CEMP) stars in the Galactic halo. A fine tuning of the model parameters for individual stars is required to reproduce the observed ratios of carbon to iron. We focus on extremely metal-poor stars formed out of the ejecta from the mixing and fallback models using a chemical evolution model. Our chemical evolution models take into account the contribution of individual stars to chemical enrichment in host halos together with their evolution in the context of the hierarchical clustering. Parametrized models of mixing and fallback models for Pop. III faint supernovae are implemented in the chemical evolution models with merger trees to reproduce the observed CEMP stars. A variety of choices for model parameters on star formation and metal-pollution by faint supernovae is unable to reproduce the observed stars with [Fe/H] < -4 and [C/H] > -2, which are the majority of CEMP stars among the lowest metallicity stars. Only possible solution is to form stars from small ejecta mass, which produces an inconsistent metallicity distribution function. We conclude that not all the CEMP stars are explicable by the mixing and fallback models. We also tested the contribution of binary mass transfers from AGB stars that are also supposed to reproduce the abundances of known CEMP stars. This model reasonably reproduces the distribution of carbon and iron abundances simultaneously only if we assume that long-period binaries are favored at [Fe/H] < -3.5.
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