A horticulturist is designing a study to investigate the effectiveness of five methods for the irrigation of blueberry shrubs. The methods are surface, trickle, center pivot, lateral move, and subirrigation. There are 10 blueberry farms available for the study, representing a wide variety of types of soil, terrains, and wind gradients. The horticulturist wants to use each of the five methods of irrigation on all 10 farms to moderate the effect of the many extraneous sources of variation that may impact the blueberry yields. On each farm, five 1- acre plots are randomly selected, and a method of irrigation is randomly assigned to each plot. The response variable will be the weight of the harvested fruit from each of the plots of blueberry shrubs.
a. Show the details of how you would randomly assign the five methods of irrigation to the plots.
b. How many different arrangements of the five methods of irrigation are possible in each of the farms?
c. How many different arrangements are possible for the whole study of 10 farms?