Sammy’s Pizza Shop offers 2 different pizza crusts, 3 different cheeses, and 8 different toppings. How many combinations of pizza can be ordered?
The standard answer is 2*3*8=48 different combinations,assuming that customers always take one cheese and one topping, and of course, one crust.
The practical answer to the question would, however, take into account that customer can take 0 to 3 cheeses, 0 to 8 toppings, but only one crust.
For cheeses, the cardinality of the power set (all possibilities) is 2^3, namely:
none,
A,
B,
C,
A+B,
A+C,
B+C,
A+B+C.
The same goes for toppings, i.e. 2^8=256 combinations.
Therefore the number of pizza combinations is:
2 crusts*8 cheeses * 256 toppings
= 4096 combinations.
How many combinations of hamburgers can you have with 12 toppings?
To find out the number of combinations of pizza that can be ordered, we need to multiply the number of options for each choice.
First, let's consider the crust options. Since there are 2 different crusts, you have 2 choices for the crust.
Next, let's move on to the cheese options. With 3 different kinds of cheese, you have 3 choices for the cheese.
Lastly, let's consider the toppings. With 8 different toppings available, you have 8 choices for each topping.
To calculate the total number of combinations, multiply the number of choices for each category together: 2 (crust options) * 3 (cheese options) * 8 (topping options).
2 * 3 * 8 = 48
Therefore, there are 48 different combinations of pizza that can be ordered from Sammy's Pizza Shop.