1. A television commercial for Little Caesars pizza announced that with the purchase of two pizzas, one would receive free any combination of up to five toppings on each pizza. The commercial shows a young child waiting in line at Little Caesars who calculates that there are 1,048,576 possibilities for the toppings on the two pizzas.

a. verify the child's calculation. Use the fact that little Caesars has 11 topping to choose from. Assume that the order of the two pizzas matters;that is if the first pizza has a combination of 1 and second pizza has combination of 2, that is different from combination 2 on the first pizza and combination 1 on the second.

b. In a letter to the mathematics teacher, Joseph F.Heiser argued that the two combinations described in part a should be counted as the same, so the child has actually over counted. Give the number of possibilities if the order of two pizzas doesn't matter.

2. A controversy arose in 1992 over the teen talk Barbie doll, each of which was programmed with four saying randomly picked from a set of 270 sayings. The controversy was over saying ," Math class is tough", which some felt gave a negative message toward girls doing well in math. In an interview with science, a spokeswoman for Mattel, the makers of Barbie, said that " There's a less than 1% chance, you're going to get a doll that says math class is tough." Is this figure correct? If not give the correct figure.