Question

Suppose that a pizza parlor features four specialty pizzas and pizzas with three or fewer unique toppings (no choosing anchovies twice!) chosen from 17 available toppings. How many different pizzas are there?

Answer 1

Pizzas with no topping: 4
Pizzas withne one topping: 4*17
Pizzas with two toppings: 4*17*16
Pizzas with three toppings: 4*17*16*15

$N=4+4*17+4*17*16+4*17*16*15=17480.$