QPizza Varieties A television commercial for Little Caesars
pizza announced that with the purchase of two pizzas, one
could receive free any combination of up to five toppings
on each pizza

Pizza Varieties A television commercial for Little Caesars

pizza announced that with the purchase of two pizzas, one

could 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 toppings to choose from. Assume that the

order of the two pizzas matters; that is, if the first pizza

has combination 1 and the second pizza has combination

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 the two pizzas doesn’t matter.