Permutate the ingredients.

3 cheeses * 4 meats * 5 vegetables = <<3*4*5=60>>60 choice

However, we must take out the combinations that could have pepperoni and peppers, 1 cheese +1 meat *+1 vegetable = <<1+1+1=3>>3 bad choices

60 - 3 = <<60-3=57>>57 choices

# Answer

57
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Denmark wants to order pizza.  For toppings, he has 3 cheese, 4 meat and 5 vegetable options, one of which is peppers. He can have only one selection from each topping category (one cheese, one meat and one vegetable). However, if he chooses to have pepperoni, he cannot have peppers. How many topping combinations does he have total?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
57
Denmark wants to order pizza.  For toppings, he has 3 cheese, 4 meat and 5 vegetable options, one of which is peppers. He can have only one selection from each topping category (one cheese, one meat and one vegetable). However, if he chooses to have pepperoni, he cannot have peppers. How many topping combinations does he have total?
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