2. Ebony and her sister want to open a store where children can buy a doll that they can personalize themselves. They plan to name the store “Make a Friend!” Children purchasing a doll at the store can choose the doll’s hair color, as well as an outfit that consists of a top and a bottom. The possible choices are: Hair color: brown, black, or blonde Top: pink ruffle blouse, blue tank top, black T-shirt Bottom: Pink skirt, blue jeans, black pants, brown shorts (a) How many different unique dolls are possible? Show your work. (b) What are all the possible combinations of hair color, tops, and bottoms? Use a tree diagram or an organized list. (c) Ebony wants to advertise that there are at least 100 different types of dolls available. If she adds another category to make this advertisement true, what is the minimum number of options she will need in this new category? Explain your reasoning. (d) Ebony’s sister says she wants to keep costs down by making sure they add the fewest number of options needed to make the above advertisement true. She believes it would be better to just increase the number of options in each of the current categories. Is Ebony’s sister right? Explain your reasoning. (e) Ebony comes up with a fun promotion called “Mismatch Day,” using the current options. The promotion gives customers a 10% discount if they choose an outfit in which the colors of the top and the bottom do not match. How many fewer choices of dolls do customers have if they take advantage of this promotion? Show your work.