If a pizza could have some (or none) toppings out of cheese, pepperoni, ham, sausage, and mushrooms. How many different kinds of such pizzas can be made? Assume order of toppings does not matter and assume for each toping either it has it or it does not.
A set of n elements has 2^n subsets.
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To determine the number of different kinds of pizzas that can be made with the given toppings, we need to consider the number of options for each topping (yes or no) and multiply them together.
In this case, we have five possible toppings: cheese, pepperoni, ham, sausage, and mushrooms. For each topping, we can either include it or exclude it.
For example, let's start with the first topping, cheese. We have two options: we can either include it or exclude it. The same goes for the rest of the toppings: pepperoni, ham, sausage, and mushrooms.
Since each topping can be either included or excluded independently, we can use the concept of combinations to calculate the total number of different kinds of pizzas. The number of combinations can be calculated using the formula 2^n, where n is the number of toppings.
In this case, we have 5 toppings, so the total number of different kinds of pizzas is 2^5 = 32.
Therefore, there are 32 different kinds of pizzas that can be made with the given toppings, assuming the order of toppings does not matter and each topping can be either present or absent.