Arguing about a homework problem correctness 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?
 A: I assume that your answer is gotten from the rational that you don't have to buy any particular thing (so there is an option for no soup for example hence the (3+1) term). Finally you subtract 1 because you assume that you have to order something (the choice of 3 nulls you are subtracting). For this specific rational you answer is correct. As for why your teacher marked off I would have to ask what did the teacher mean. For example is it possible to buy nothing...? 
A: Here are the options:
soup, dinner, desert: 108 (multiply individual options)
No soup, dinner, desert: 36 choices
Soup, no dinner, desert: 12 choices
Soup, dinner, no desert: 27 choices
no soup, no dinner, desert: 4 choices
no soup, dinner, no desert: 9 choices
soup, no dinner, no desert: 3 choices:
no soup, no dinner, no desert: 1 choice
Total 200. 
If not, I either misinterpret the question or I made a mistake I would like to have explained. Either way, the teacher should give a thorough explanation what she thought is the right way.
