\[\boxed{\mathbf{117.}}\]
\[\textbf{а)}\ \frac{1}{3} \cdot \frac{1}{3} + \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{2} = \frac{1}{9} + \frac{1}{18} =\]
\[= \frac{2}{18} + \frac{1}{18} = \frac{3}{18} = \frac{1}{6}.\]
\[\textbf{б)}\ \frac{1}{3} \cdot \frac{1}{3} + \frac{1}{3} \cdot \frac{1}{3} \cdot \frac{1}{2} = \frac{1}{9} + \frac{1}{18} = \frac{1}{6}.\]
\[\textbf{в)}\ \frac{1}{3} \cdot \frac{1}{2} + \frac{1}{3} \cdot \frac{1}{3} = \frac{1}{6} + \frac{1}{9} =\]
\[= \frac{3}{18} + \frac{2}{18} = \frac{5}{18}.\]
\[\textbf{г)}\ \frac{1}{6} + \frac{1}{3} \cdot \frac{1}{3} = \frac{1}{6} + \frac{1}{9} = \frac{5}{18}.\]