I have an ordered sequence with $n$ elements: $\{1,...,n\}$. I would like to obtain all the possible combinations of $m$ elements using just the first half of $n$ (so the numbers from $0$ to $n/2$). I feel that just ${\frac{n}{2}\choose m}$ does not return the fact that I want the first half of the set.
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Why shouldn't it? Restrict your set to ${1,..., \frac{n}{2} }$ and forget about your initial set. Or have I misunderstood the question? – LuxGiammi Oct 17 '18 at 15:08
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1Assuming $n$ is even? – Randall Oct 17 '18 at 15:09
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Well, if n is not even I suppose GYBE for "the first half" intends $\frac{n-1}2$ or $\frac{n+1}2$ – LuxGiammi Oct 17 '18 at 15:10