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Suppose that a pizza parlor features four specialty pizzas and pizzas with three or fewer unique
toppings (no choosing twice!) chosen from 17 available toppings. How many different pizzas are there?
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4 pizzas with no topping, PLUS
4*17 pizzas with one topping PLUS
4*17*16 pizzas with two toppings PLUS
4*17*16*15 pizzas with three toppings
the total = 4 + 4*17 + 4*17*16 + 4*17*16*15 = 17480 different pizzas. ANSWER
Solved and explained.