Concept:
Colour in transition metal ions arises due to \(d\text{-}d\) transitions, which occur only when the \(d\)-orbital is partially filled (not \(d^0\) or \(d^{10}\)).
Step 1: Electronic configurations:
\[
\mathrm{Cu^{2+}} : [\mathrm{Ar}] \, 3d^9 \quad \text{(partially filled → coloured)}
\]
\[
\mathrm{Fe^{3+}} : [\mathrm{Ar}] \, 3d^5 \quad \text{(partially filled → coloured)}
\]
\[
\mathrm{Ti^{3+}} : [\mathrm{Ar}] \, 3d^1 \quad \text{(partially filled → coloured)}
\]
\[
\mathrm{Zn^{2+}} : [\mathrm{Ar}] \, 3d^{10} \quad \text{(fully filled → colourless)}
\]
Step 2:
Number of coloured ions = \(3\)