I've recently completely a homework in a problem solving class, I think my reasoning is correct but my teacher insisted that my answer is incorrect. I'm not sure if I'm correct or not.
Question: You're going into a restaurant for dinner and you're getting at most one soup, at most one main dish and at most one dessert. In fact, the restaurant offers 3 different soups, 9 different main dishes and 4 different desserts. How many ways can you order?
My answer: $(3+1)*(9+1)*(4+1)-1=199$
My explanations with my answer: Since it's possible not to order a soup, a main dish and/or a dessert, therefore there're 4 ways to choose the soup, 10 ways for the main dish and 5 ways for the dessert.
However, I receive a big fat X on my answer and received no points. I asked teacher for further explanations she said that's it's not even making any sense how I got my answer.
Can anyone point out what I did wrong (if there is something wrong)? thanks!
Update: My teacher said that the correct answer should be 108 because the total combinations should be 3*9*4=108. The question is exactly worded as above. Do you think I should talk with an academic supervisor with this or not?