# 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?

• Why subtract $1$? Sep 1, 2013 at 21:10
• Did you include your explanations in the homework that you submitted to your teacher? Sep 1, 2013 at 21:10
• Anyway, in my opinion, presenting the answer simply as $(3+1)(9+1)(4+1)$ is self-explanatory. Sep 1, 2013 at 21:15
• Maybe not ordering anything is not so uncommon an option at all - for example you might find out that all they offer is to expensive or would cause allergic reactions or simply does not appeal you Sep 1, 2013 at 21:28
• If you stated the problem correctly, the correct answer is unquestionably $200$ or $199$, depending on whether you’re allowed to order nothing at all. If the answer that the teacher wants is not one of these, she’s simply wrong. If she wants $200$, I think that awarding no marks for your answer is unduly harsh, since you plainly did understand the main point of the problem; it would, however, have been better to have explained why you were subtracting $1$. Sep 1, 2013 at 23:41