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Sammy’s Pizza Shop offers 2 different pizza crusts, 3 different cheeses, and 8 different toppings. How many combinations of pizza can be ordered?

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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.

• math -

How many combinations of hamburgers can you have with 12 toppings?

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