Question 61
Let $n$ be a positive integer. Prove that there is an odd number of odd numbers among the numbers
$$
\binom{2n+1}{1}, \binom{2n+1}{2}, \dots, \binom{2n+1}{k}, \dots, \binom{2n+1}{n}.
$$
$$
\binom{2n+1}{1}, \binom{2n+1}{2}, \dots, \binom{2n+1}{k}, \dots, \binom{2n+1}{n}.
$$