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I'm preparing for a test but I do not have the solutions available (as there are no solutions). It would be nice if someone could point out whether I solved the following exercise correctly.

Question: 11 people are going to dinner at a fancy restaurant. Every person is very hungry so everyone decides to take an entree, main dish and dessert. There is not much choice though: 2 choices for the entree, 3 for the main dish and 2 for the dessert. A waitress makes a list with all the dishes (in total 7) and how many times this dish is ordered. How many possible lists can the waitress make?

Solution

I believe this uses combinations with repitition:

The solution then would be:

$$\binom{12}{11} \binom{13}{11} \binom{12}{11} = 11232 $$

Could someone verify this solution please?

Thanks in advance :)

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Your answer is correct. We can analyze the possibilities for each course independantly using stars and bars.

There are $\binom{12}{11}$ posssibilities for the entree, $\binom{13}{11}$ for the main dish and $\binom{12}{11}$ for the dessert.

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