Combination of m elements from the first half of an ordered set

Question

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.