The original toy cost $0.98, and contained hands, feet, ears, two mouths, two pairs of eyes, four noses, three hats, eyeglasses, a pipe, and eight felt pieces resembling facial hair. The original Mr. Potato Head kit did not come with a potato “body”, so parents had to provide their own potato into which children could stick the various pieces. Shortly after the toy’s initial release, an order form for 50 additional pieces was enclosed in every kit.
1. How many different looks could be made using the original toy (described above), if you use the hands for hands, the ears for ears, etc., and he had a pair of hands, a pair of feet, a pair of eyes, a pair of ears, a nose, a mouth, hair and nothing else? (Note: all pairs are matched)
2. If you included the option of a hat, glasses, and/or a pipe (i.e. they could be included or not, and each different hat was considered a separate option), how many different looks could you create?
3. Different sets have different options. For example, initially, you could order a package of 50 additional pieces. Create a generic formula (using variables) to compute the number of different Mr. Potato Head looks possible (presuming that the only items possible are hands, feet, ears, eyes, noses, mouths, hats, glasses, pipes, and hair), if you assumed that all paired items were the same (i.e. matched arms). You are welcome to define single letter variables for each option, or include words in your equation (i.e. [# eye options]*3or 3E) (If you use single letter variable, provide a key). Explain how you arrived at your equation. Note: we will talk about a process that can be used to create an equation in class.