Question

A pizza restaurant offers 6 different pizza toppings and 3 different sizes. How many different pizzas are possible if a patron of the restaurant can pick any size pizza and any number of toppings 0-6 (assume no double toppings )?

Answer 1

There are 192 different pizzas possible if a patron can pick any size pizza and any number of toppings 0-6.

Step-by-step explanation:

In this case, there are 6 different toppings and 3 different sizes of pizza. Since a patron can pick any number of toppings from 0 to 6, we can think of this problem as selecting toppings from a set of 6 options, with repetitions allowed. For each topping, the patron can either choose to include it on the pizza or not, giving 2 choices. Therefore, the total number of possible combinations of toppings is 2 raised to the power of 6, which is equal to 64.

For each combination of toppings, the patron can then choose any of the 3 different sizes of pizza. So, for each combination of toppings, there are 3 different size options. Therefore, the total number of different pizzas possible is 64 multiplied by 3, which is equal to 192.