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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?

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    $\begingroup$ Why subtract $1$? $\endgroup$
    – Git Gud
    Sep 1, 2013 at 21:10
  • $\begingroup$ Did you include your explanations in the homework that you submitted to your teacher? $\endgroup$
    – Michael Albanese
    Sep 1, 2013 at 21:10
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    $\begingroup$ Anyway, in my opinion, presenting the answer simply as $(3+1)(9+1)(4+1)$ is self-explanatory. $\endgroup$
    – Git Gud
    Sep 1, 2013 at 21:15
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    $\begingroup$ 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 $\endgroup$
    – Hagen von Eitzen
    Sep 1, 2013 at 21:28
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    $\begingroup$ 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 $1$. $\endgroup$
    – Brian M. Scott
    Sep 1, 2013 at 23:41

2 Answers 2

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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.

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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...?

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  • $\begingroup$ Yes that's my reasoning, however my teacher didn't provide me with the correct answer, other than a big fat X; so the answer is either 200 or 199 no matter "rational" or not right? $\endgroup$
    – Commander Shepard
    Sep 1, 2013 at 21:17
  • $\begingroup$ It's hard to determine what was in your teacher's mind. For example instead of at most one perhaps she meant exactly one. If you say that you don't want points back but want to understand what she was asking then she should definitely explain it to you. $\endgroup$
    – Owen Sizemore
    Sep 1, 2013 at 21:21

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