Prove parity of binomial coefficient The task is to find the parity of ${2n\choose 2k+1}$ where $n,k\in\mathbb{N}$. How can I do that?

Hint $\rm\displaystyle\  \ k {n\choose k} =\ n {n-1 \choose k-1 }\:$ so $\rm\:k\:$ odd, $\rm\:n\:$ even $\:\displaystyle\rm\Rightarrow {n \choose k}\:$ is $\:\ldots$
For the parity of the general case see here.
