You run pizza shop and have 8 different toppings that a customer can order. The customer can order any combination of topping including none but they cannot have double of any toppings. How many different pizza combinations can be ordered?
This becomes a question of the number of subsets with 8 elements.
number of subsets = 2^8 or 256
Notice that this would include the nullset, correponing with "no items" and the the set of all elements, your "loaded pizza"
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To find the number of different pizza combinations that can be ordered, we need to consider the choices for each topping. Since a customer can choose any combination of toppings including none, we have two possibilities for each topping:
1. The customer includes the topping on their pizza.
2. The customer does not include the topping on their pizza.
Therefore, for each topping, there are 2 choices. Since we have 8 different toppings, the total number of combinations can be found by multiplying these choices together:
2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^8 = 256.
Hence, there are 256 different pizza combinations that can be ordered from your pizza shop, considering that the customer can include any combination of toppings or choose none at all.