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Possible Duplicate:
How to reverse the $n$ choose $k$ formula?

Recently saw an ad for a salad bar in Spain offering 1000 different combinations. Now, this could be a salad containing three parts, with a choice of ten ingredients for each part, but this was probably just an advertisement effort. There is one more (unlikely) option that I found interesting:

The salad bar could potentially have $n$ ingredients, from which you could choose only $m$, if the following condition held:

${m \choose n } = \frac{n!}{m!(n-m)!} = 1000$

And more generally, for a given $N$, do there exist $m,n$ such that: ${m \choose n } = N$ Is there a general method of finding such a pair? is such a pair unique?

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    In related news, I recently visited [a gelato store](http://www.lacasagelato.com/) that advertises 218 flavors. I counted the tubs and found that there were actually 224 different flavors on sale. I asked why all the signage proclaimed 218; the attendant said “in case we run out of some”.2015-01-12

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