The complex \( [Co(NH_3)_6]Cl_2 \) consists of a coordination sphere \( [Co(NH_3)_6]^{2+} \) and 2 chloride ions \( Cl^- \) outside the coordination sphere. When this complex dissolves in water, it dissociates as follows:
\[
[Co(NH_3)_6]Cl_2 \rightarrow [Co(NH_3)_6]^{2+} + 2Cl^-
\]
Thus, the total number of ions generated is:
- 1 ion of \( [Co(NH_3)_6]^{2+} \),
- 2 ions of \( Cl^- \).
The total number of ions = 1 + 2 = 3 ions.
Therefore, the correct answer is option (C) 3.