A substantial fraction of the lowest metallicity stars show very high enhancements in carbon. It is debated whether these enhancements reflect the stars' birth composition, or if their atmospheres were subsequently polluted, most likely by accretion from an AGB binary companion. Here we investigate and compare the binary properties of three carbon-enhanced sub-classes: The metal-poor CEMP-s stars that are additionally enhanced in barium; the higher metallicity (sg)CH- and Ba II stars also enhanced in barium; and the metal-poor CEMP-no stars, not enhanced in barium. Through comparison with simulations, we demonstrate that all barium-enhanced populations are best represented by a ~100% binary fraction with a shorter period distribution of at maximum ~20,000 days. This result greatly strengthens the hypothesis that a similar binary mass transfer origin is responsible for their chemical patterns. For the CEMP-no group we present new radial velocity data from the Hobby-Eberly Telescope for 15 stars to supplement the scarce literature data. Two of these stars show indisputable signatures of binarity. The complete CEMP-no dataset is clearly inconsistent with the binary properties of the CEMP-s class, thereby strongly indicating a different physical origin of their carbon enhancements. The CEMP-no binary fraction is still poorly constrained, but the population resembles more the binary properties in the Solar Neighbourhood.

13 pages, 7 figures, accepted for publication in MNRAS