Iron corrode in the presence of Copper but not in the presence of Zinc. 

On moving from bottom to top of the series, the tendency to lose electrons increases and hence, the oxidizing nature of metals increases. 

Copper lies below Iron in the reactivity series, hence, Iron is more oxidizable/ reactive metal than copper. Hence, iron corrodes in the presence of copper. While Zinc lies above Iron in the reactivity series and is more reactive than iron. Thus, in the presence of Zinc, iron does not corrode.