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We report inclusive and exclusive measurements for ${\ensuremath{\chi}}_{c1}$ and ${\ensuremath{\chi}}_{c2}$ production in $B$ decays. We measure $\mathcal{B}(B\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c1}X)=(3.03\ifmmode\pm\else\textpm\fi{}0.05(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.24(\mathrm{syst}))\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $\mathcal{B}(B\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c2}X)=(0.70\ifmmode\pm\else\textpm\fi{}0.06(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}0.10(\mathrm{syst}))\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. For the first time, ${\ensuremath{\chi}}_{c2}$ production in exclusive $B$ decays in the modes ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c2}{\ensuremath{\pi}}^{\ensuremath{-}}{K}^{+}$ and ${B}^{+}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c2}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{K}^{+}$ has been observed, along with first evidence for the ${B}^{+}\ensuremath{\rightarrow}{\ensuremath{\chi}}_{c2}{\ensuremath{\pi}}^{+}{K}_{S}^{0}$ decay mode. For ${\ensuremath{\chi}}_{c1}$ production, …