Need an explanation. Details in chat. Here is the problem:

Luigi's Pizza Shop offers three types of crust, five types of toppings, and four types of cheese. Suppose a pizza at Luigi's consists of a crust and at least one type of cheese; it may have no toppings, one topping, or more than one topping, as well as more than one cheese. How many different types of pizza can be made: 1. with exactly 5 toppings and 4 cheeses? 2. with exactly 3 toppings and 2 cheeses? 3. with exactly 2 toppings and 3 cheeses? 4. with exactly 2 toppings and 4 cheeses? 5. with exactly 3 toppings? 6. with exactly 4 toppings? 7. with exactly 4 cheeses? 8. with at least two cheeses? 9. with at most four toppings? 10. with at least two cheeses and at most four toppings? 11. in total?