Suppose that the pizza shop of Example 2.20 adds a new possible topping, sardines, but insists that each pizza either have sardines or have anchovies. How many possible varieties of pizza does the shop now offer?

There are 10 toppings in total. There are \(2^8 = 256\) pizzas with sardines + any subset of remaining 8 toppings (excluding anchovies since we cannot have sardines and anchovies in the same pizza) and \(2^8 = 256\) pizzas with anchovies + any subset of remaining 8 toppings (excluding sardines, since we cannot have anchovies and sardines in the same pizza) for the total of \(2 \cdot 2^8 = 2^9 = 512\) varieties of pizza.