An increasing fraction of carbon-enhanced metal-poor (CEMP) stars is found as their iron abundance, [Fe/H], decreases below [Fe/H] = -2.0. The CEMP-s stars have the highest absolute carbon abundances, [C/H], and are thought to owe their enrichment in carbon and the slow neutron-capture (s-process) elements to mass transfer from a former asymptotic giant-branch (AGB) binary companion. The most Fe-poor CEMP stars are normally single, exhibit somewhat lower [C/H] than CEMP-s stars, but show no s-process element enhancement (CEMP-no stars). CNO abundance determinations offer clues to their formation sites. C, N, Sr, and Ba abundances (or limits) and 12C/13C ratios where possible are derived for a sample of 27 faint metal-poor stars for which the X-shooter spectra have sufficient S/N ratios. These moderate resolution, low S/N (~10-40) spectra prove sufficient to perform limited chemical tagging and enable assignment of these stars into the CEMP sub-classes (CEMP-s and CEMP-no). According to the derived abundances, 17 of our sample stars are CEMP-s and three are CEMP-no, while the remaining seven are carbon-normal. For four CEMP stars, the sub-classification remains uncertain, and two of them may be pulsating AGB stars. The derived stellar abundances trace the formation processes and sites of our sample stars. The [C/N] abundance ratio is useful to identify stars with chemical compositions unaffected by internal mixing, and the [Sr/Ba] abundance ratio allows us to distinguish between CEMP-s stars with AGB progenitors and the CEMP-no stars. Suggested formation sites for the latter include faint supernovae with mixing and fallback and/or primordial, rapidly-rotating, massive stars (spinstars). X-shooter spectra have thus proved to be valuable tools in the continued search for their origin. Abridged.
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