How many different pizzas can be ordered if the restaurant offers 15 different toppings and there is no limit to the number of toppings on the pizza
If there are no limits to the number of toppings on a pizza, then each topping can either be chosen or not chosen for inclusion on the pizza.
For each topping, there are two possibilities: it can be chosen or not chosen. This means that for each topping, there are 2 options.
Since there are 15 different toppings, there will be a total of 2^15 = 32,768 different possible combinations of toppings. Therefore, there can be 32,768 different pizzas that can be ordered.
To calculate the number of different pizzas that can be ordered with 15 different toppings and no limit to the number of toppings, we can use the concept of combinations.
Since each topping can be either present or absent on the pizza, we have 2 options for each topping - to include it or not include it. Therefore, for each of the 15 toppings, we have 2 choices - a total of 2^15 choices.
Using this logic, we can determine that there are 2^15 = 32,768 different pizzas that can be ordered with 15 different toppings and no limit on the number of toppings.