Answer:
It could either be 455 or 680, based on assumptions.
Step-by-step explanation:
Assuming the three choices are distinct, we can calculate...
15C3 = 15·14·13/(3·2·1) = 35·13 = 455
ways to create the pizza.
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In the case where two or more of the toppings may be identical, this would lead to...
2(15C2) + 15C1 = 2·105 + 15 = 225
additional combinations, resulting in a grand total of...
455 + 225 = 680
unique pizza varieties.
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There is a multiplication factor of 2 for the two-topping selections, since it allows for variations like double anchovies and tomatoes or double tomatoes and anchovies when the topping choices are anchovies and tomatoes.
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nCk = n!/(k!(n-k)!)