The Ultraviolet Coronagraph Spectrometer on board the Solar and Heliospheric Observatory (SOHO) observes low ionization state coronal mass ejection plasma at ultraviolet wavelengths. The CME plasmas are often detected in O VI ($3{ imes}10^5K$), C III ($8{ imes}10^4K$), $Ly{alpha}$, and $Ly{eta}$. Earlier in situ observations by the Solar Wind Ion Composition Spectrometer (SWICS) on board Advanced Composition Explorer (ACE) have shown mostly high ionization state plasmas in interplanetary coronal mass ejections (ICME) events, which implies that most CME plasma is strongly heated during its expansion in solar corona. In this analysis, we investigate whether the low ionization state CME plasmas observed by UVCS occupy small enough fractions of the CME volume to be consistent with the small fraction of ICMEs measured by ACE that show low ionization plasma, or whether the CME must be further ionized after passing the UVCS slit. To do this, we determine the covering factors of low ionization state plasma for 10 CME events. We find that the low ionization state plasmas in CMEs observed by UVCS show small covering factors. This result shows that the high ionization state ICME plasmas observed by the ACE results from a small filling factor of cool plasma. We also find that the low ionization state plasma volumes in faster CMEs are smaller than in slower CMEs. Most slow CMEs in this analysis are associated with a prominence eruption, while the faster CMEs are associated with X-class flares.