I got this question right by guessing and im not entirely sure I understand Greg’s solutions. He uses the multiplication principle to derive 232^5. I understand the first product but im not sure where the 2^5 comes from? Is it because for any given topping it can be either on the pizza or not? If so I understand the question as saying there are 5 toppings, which can be arbitrarily combined which led to using the expressions 23((5 choose 1) + (5 choose 2) +…+(5 choose 5))
With topping: we can either choose it or ignore it (so, either a topping is on pizza(1) or it isn’t(0)).Since, each topping has two possibilities (1 or 0), and we have 5 toppings, we have: 2^5 = 32
In the case of the cheese and crust, we’re selecting one item from a set without repetition - this is a combination. However, with the toppings, we’re not just selecting items from a set, we’re also considering the possibility of not selecting each item. This is why we use the concept of permutations with repetition.