Di is opening a new hardware store selling nuts, bolts, and everything in between: "You'll bolt to our store because our prices are nuts!". Di is organizing one section of the store, which will showcase the many different types of bolts available. There are thirteen sizes of bolts, each available in seven different types of material.15 (a) Di will have a bin for each possible combination of bolt size and material. How many bins will Di need in order to set up the bolt display? (b) Di wants to organize the bins of bolts into rows. Each row will be placed on one of seven shelves, arranged from top to bottom. Di wants each row to contain all the bolts of a single material. Within each row, all 13 sizes of bolts of that material will be placed in some order. Di wants the ordering of sizes to be the same for all rows, but is considering any possible ordering. How many possible arrangements of the bins are there? (c) What if Di no longer insists that each row have the same ordering for the sizes? That is, Di wants to have all the bins for bolts of a given material in the same row (giving seven rows total, arranged in some order from top to bottom), and will ar- range the sizes within each row separately (so that the ordering of sizes in each row may be different). How many possible arrangements of the bins are there now?