There are 7C5 = 7*6/(2*1) = 21 pizzas.
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8C3 = 8*7*6/(3*2*1) = 56
You can make 28 = 256 pizzas. Topping 1: You either have it or you don't: two choices. With each choice, for topping 2: You either have it or you don't: two choices. That makes 2*2 or 22 choices. With each choice for the first two, for topping 3: You either have it or you don't: two choices. That makes 2*2*3 or 23 choices. and so on, making 28 choices in all. Note that one choice will comprise no toppings.
32 combinations. 4 of these will have no toppings, or all three toppings, 12 will have one topping and another 12 will have 2 toppings.
three
2*2*2*2 = 16, counting one with no toppings.