# 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?

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Could you be more specific about what it is you seek to prove? "The parity of $\binom{2n}{2k+1}$" is not a claim that can be true or false, so it is not a priori something it makes sense to prove. –  Henning Makholm Mar 3 '12 at 22:55

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 $\:\ldots$