A local pizzeria offers 15 toppings for their pizzas and you can choose any 3 of them for one fixed price. How many different ty

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)!)