Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have the following homework, for which I'd like you to give me some hints. Thank you.

There are M food dishes and N bottles of different wines. There are 4 ways to pair food and wine: 1 (dish) to 1 (type of wine), 1 to many, many to 1, and many to many. A menu must use all M dishes and N wine bottles. How many possible menus can one make?

share|improve this question

migrated from stats.stackexchange.com Mar 2 '11 at 6:10

This question came from our site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.

1  
(a) The problem might look familiar when you think of "food dishes" as a sequence of $M$ blanks to fill in and "wines" as $N$ distinct digits $0, 1, \ldots, N-1$. For example, what does the question ask (in these terms) when $N=10$? (b) You need to decide how to interpret the statement. Is it four different questions or one? –  whuber Feb 28 '11 at 22:29
2  
This is combinatorics rather than probability or statistics, so it might be better at math.SE –  onestop Mar 1 '11 at 10:18

1 Answer 1

I don't understand "There are 4 ways to pair food and wine: 1 (dish) to 1 (type of wine), 1 to many, many to 1, and many to many" If you have a number of courses, you need that many dishes and that many wines. The naive answer is that you can pair n wines with the first dish, n-1 with the next, and so on, leading to n! choices. But that doesn't respect the 4 ways to pair food and wine. What am I missing?

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.