Question: Let's say you own a construction company. Answer the following three questions.

a. A housing community forbids look-a-like homes on the same street. A new cul-de-sac street in this community has 7 lots, all of which are empty. If your construction company has 10 suitable home designs for this street, how many ways can a set of 7 of them be selected?

b. For a particular home design's exterior, you offer the customer a choice of three types of shutters, 5 types of siding (aluminum, brick, concrete blocks, wood, or stone), and two types of roof shingles (ceramic tiles or tar). How many ways can a customer select one type of shutter, and one type of siding, and one type of roof shingles?

c. The n homes in your original sample are to be renovated and your construction company has been hired for this job. On Monday, you want to make a quick survey of two randomly selected homes from the n. How many ways can two of your n homes be randomly selected and then slated into two time slots: a morning slot, and an afternoon slot?