Little Caesar's Pizza had a commercial on television that claimed you could buy one pizza and get another one free, with up to 5 toppings per pizza (do not count the pizza sauce or the cheese as a topping). The dialogue on the commercial went something like this. The tall person said, "5 toppings per pizza; that's 10 different pizzas to choose from." The little guy then said, "No, it's 1,048,576 pizzas." What do you think?
The dialogue in the commercial you mentioned involves a calculation regarding the number of different pizzas you can create when you have the option to choose up to 5 toppings per pizza. The tall person suggests that there are 10 different pizzas to choose from, while the little guy counterclaims that there are actually 1,048,576 pizzas. Let's explore how they arrived at these numbers:
To calculate the number of different pizzas, we need to consider the number of possible choices for each topping. Assuming there are multiple topping options available, let's assume there are 10 choices for each topping (this seems to be in line with the conversation in the commercial).
If we can choose up to 5 toppings per pizza, this means we need to multiply the number of choices for each topping together. In this case, it would be 10 * 10 * 10 * 10 * 10, which equals 100,000 different pizzas.
So, according to the tall person, there would be 100,000 different pizzas to choose from. However, the little guy claims there are actually 1,048,576 pizzas.
Now, let's figure out how the little guy arrived at this number. It seems he utilized the concept of combinations where the specific order of the toppings does not matter. Since there are 10 choices for each topping, the number of possible combinations would be 10^5 or 1,000,000. However, this includes the case where no toppings are chosen, which doesn't meet the criteria stated in the commercial.
Since pizzas with no toppings are not counted in this scenario, we must subtract 1 from the total number of combinations. Therefore, 1,000,000 - 1 equals 999,999 different pizzas.
However, the little guy claimed there are 1,048,576 pizzas. This number can be obtained if we include the possibility of having no toppings on our pizza. By adding one more option, where no toppings are chosen, we can generate all possible combinations. This is known as the power set. In this case, it is 2^5 which equals 32.
So, by the little guy's calculation, it seems that he assumed there were 32 different options for each of the 100,000 different pizzas. Therefore, 32 * 100,000 equals 3,200,000 different pizzas. However, we need to subtract 1 from this total to account for the case of no toppings, which brings us to 3,199,999 pizzas. It's important to note that the exact value mentioned in the commercial is 1,048,576 and not 3,199,999, so there might be some discrepancy or error in the dialogue presented.
In conclusion, the tall person claimed there were 100,000 different pizzas to choose from, while the little guy claimed there were 1,048,576 (or 3,199,999 according to our analysis). It seems there was some confusion or misunderstanding in the dialogue regarding the calculation.