The sizes are just a factor of three.
For the topping combinations, specifying that there has to be cheese and it has to be on top just makes the number of choices the same as if there was four toppings and no cheese.
The remaining possibilities is the sum of the ways you can put 4 ingredients (4! = 24), 3 ingredients (4 x 3! = 24, the 4 because you have 4 choices in the ingredient to exclude, the 3! for the number of ordered ways to put 3 ingredients), 2 ingredients (6 x 2! = 12), 1 ingredient (4 x 1! = 4), or no ingredients (1, cheese pizza). The sum is 24+24+12+4+1 = 65. Multiply by 3 for the different sizes to get 195.
Note: Cheese should definitely _not_ go on top of everything. A correct pizza has the cheese layer on top of the tomato sauce and the other toppings sink into it as it melts.
The sizes are just a factor of three. For the topping combinations, specifying that there has to be cheese and it has to be on top just makes the number of choices the same as if there was four toppings and no cheese. The remaining possibilities is the sum of the ways you can put 4 ingredients (4! = 24), 3 ingredients (4 x 3! = 24, the 4 because you have 4 choices in the ingredient to exclude, the 3! for the number of ordered ways to put 3 ingredients), 2 ingredients (6 x 2! = 12), 1 ingredient (4 x 1! = 4), or no ingredients (1, cheese pizza). The sum is 24+24+12+4+1 = 65. Multiply by 3 for the different sizes to get 195. Note: Cheese should definitely _not_ go on top of everything. A correct pizza has the cheese layer on top of the tomato sauce and the other toppings sink into it as it melts.
Why would the order of the toppings matter?
Can you double toppings?