Hi everyone,

I am trying to find a combinatorial proof of the following inequality:

Given integers $\displaystyle n,t $ such that $\displaystyle 0 \leq t \leq \lfloor \frac{n}{2} \rfloor$, we have $\displaystyle {n \choose t} \leq {n \choose t+1}$

By combinatorial proof I mean starting with two sets and showing the existence of an injection. Any help would be greatly appreciated!

Caveat: This problem was among other problems in graph theory. I don't know if there is any relation with graph theory at all, I just hope I got the right section of the forum

Thanks to everyone who will reply

- Tom