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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?

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

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(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
This is combinatorics rather than probability or statistics, so it might be better at math.SE –  onestop Mar 1 '11 at 10:18
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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?

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