 Solution

The stoichiometry fixes the site probabilities to $1/4$ gold and $3/4$ copper. Every site in the average crystal structure therefore has the same atomic scattering factorThe average structure factor isAt $(110)$ the bracket vanishes, while at $(111)$ it is four. HenceThe $(111)$ powder diffraction multiplicity is unchanged, so its coherent Bragg diffraction wave intensity equals the ordered value under the stated equal-lattice constant approximation.

The zero refers to the coherent Bragg diffraction peak of the average crystal structure. A random alloy can still give occupational diffuse scattering at the same scattering vector: the average of the squared amplitude includes fluctuations as well as the square of the average amplitude. Such background is not a surviving $(110)$ Bragg diffraction peak.