Jean Sherrod of Little Caesar's Enterprises, Inc., explains that an order where the first pizza is pepperoni and the second pizza is ham would be considered different from an order in which the first pizza is ham and the second pizza is pepperoni. Using this scheme, how many pizza orders are possible?

Question

Jean Sherrod of Little Caesar's Enterprises, Inc., explains that an order where the first pizza is pepperoni and the second pizza is ham would be considered different from an order in which the first pizza is ham and the second pizza is pepperoni. Using this scheme, how many pizza orders are possible? ​  ​

Quizplus · Accepted Answer

There are 8 types of pizzas to choose from (pepperoni, ham, sausage, beef, onions, green peppers, mushrooms, and black olives) and 2 pizzas per order. Using the given scheme, the order of the pizzas matters, so there are 8 choices for the first pizza and 7 choices for the second pizza (since one type of pizza has already been chosen). Therefore, the total number of possible orders is 8 x 7, which equals 56. However, since the two pizzas can be arranged in two different ways (e.g. pepperoni-ham or ham-pepperoni), we must multiply 56 by 2 to get the final answer of 112. Finally, we must raise this number to the power of 6 (since there are 6 individuals placing orders), which gives us 88,397,604. Therefore, the best choice is C.