Suppose a campus with 26 buildings is setting up a new networking system, and there are 5 potential options available for rewiring the networking infrastructure of each building.

(a) How many possible ways can the buildings be rewired if every one has its infrastructure replaced with one of the five options.

(b) Suppose only 22 buildings are being rewired, with options 1-5 being applied to 5, 5, 4, 4, and 4 buildings respectively. How many unique configurations are possible for this scenario?

(c) Suppose the scenario from (b) occurs, but each of the 5 options simply represents a different campus sub-net being allocated to groups of buildings. How many unique configurations are possible if the order of the sub-nets is unimportant (i.e. having buildings A-D on sub-net 3 and buildings E-H on sub-net 4 is indistinguishable from having buildings E-H on sub-net 3 and buildings A-D on sub-net 4)?

Briefly explain your answers in all three cases.