For the three capacitors in series \(\frac{1}{C_{e q}}=3 \times \frac{1}{C}=\frac{3}{C} ; C_{e q}=\frac{C}{3} \ldots *\) for the other two capacitors in series \(\frac{1}{C_{\text {eq }}}=2 \times \frac{1}{C}=\frac{2}{C} ; C_{e q}=\frac{C}{2} \ldots . . * *\)
Now eqn* , and eqn** above and the \(2 C\) capacitance form a parallel combination whose total capacitance is the sum given as
\begin{aligned}
&C_{T}=\frac{2 C}{1}+\frac{C}{2}+\frac{C}{3} \\
&C_{T}=\frac{12 C+3 C+2 C}{6} \\
&C_{T}=\frac{17 C}{6}
\end{aligned}