In the formation of the ammonium ion (\( \text{NH}_4^+ \)), the nitrogen atom in \( \text{NH}_3 \) shares its lone pair of electrons with a hydrogen ion (H\(^+\)), which does not have any electrons.
This forms a co-ordinate (dative) bond.
In this bond, both electrons are provided by the nitrogen atom of the ammonia molecule, making it a co-ordinate bond.
Thus, the correct answer is (c).