  We report results of a photometric survey with the WIYN telescope for carbon
stars in the M 31 dwarf spheroidal (dSph) companions And III, And V, And VI,
and And VII, as well as in the relatively isolated Local Group dSph Cetus. We
find three carbon-star candidates in And VII and one carbon star in each And VI
and Cetus. Comparing the carbon star content with other Local Group dwarf
galaxies, we argue against the presence of substantial intermediate-age stellar
populations in the all of the galaxies surveyed with the exception of And VII.
We discuss these results in the context of the origin of the Andromeda dSphs
and conclude that these are ancient galaxies, most of which ceased star
formation long before the main merger events in M31. The M31 dSphs therefore
show less diversity in star formation histories than the Galactic dSph
companions, or the M31 dE companions, as illustrated by NGC147 which was
surveyed as a calibration object. All of our dSph targets except And V have
candidate carbon stars below the tip of the RGB, which resemble CH stars found
in globular clusters. We estimate that 0.3% of stars in the dSphs are CH stars,
presumably as a result of C pollution from a binary companion. Comparisons with
CH star frequencies in globular clusters could constrain the impact of dense
environments on the frequency of this form of binary star evolution.
