Step 1: Reduction and ring‐slip.
Sodium amalgam reduces nickelocene to an anionic species that undergoes \(\eta^{5}\!\to\!\eta^{3}\) ring slip on one Cp ring.
Step 2: Protonation by ethanol.
The reduced, slipped ring is then protonated by \(\mathrm{EtOH}\), converting \(\mathrm{C_5H_5^-}\) to \(\mathrm{C_5H_7^-}\) while retaining \(\eta^{3}\)-coordination on that ring. The other ring stays \(\eta^{5}\)-bound.
Step 3: Product identity.
The resulting mixed-sandwich complex is \((\eta^{5}\text{-}\mathrm{C_5H_5})(\eta^{3}\text{-}\mathrm{C_5H_7})\mathrm{Ni}\), which matches option (C).
\[
\boxed{(\eta^{5}\text{-}\mathrm{C_5H_5})(\eta^{3}\text{-}\mathrm{C_5H_7})\mathrm{Ni}}
\]