Compute the number of subsets of set $A=\{1,2,\ldots,11\}$ that contain the same number of even and odd values, e.g. the subsets $\varnothing, \{1,2,5,8\}$ and $\{3,5,8,10\}$ should be counted, while $\{1,2,3\}$, $\{1,3,5,6\}$ and $\{1,2,\ldots,11\}$ shouldn’t.
I got $462$, but I don't know if that is the correct answer.
The way I did it is that I made two subsets: one containing all the odd numbers and one containing all the even numbers. Then, I tried to find the possible combinations that will result in $0, 2,\ldots10$ elements and added them, giving me $462$.
Best Answer
$$\{1,3,5,7,9,11\},\{2,4,6,8,10\}$$ $$\binom{6}{0}\binom{5}{0}+\binom{6}{1}\binom{5}{1}+\binom{6}{2}\binom{5}{2}+\binom{6}{3}\binom{5}{3}+\binom{6}{4}\binom{5}{4}+\binom{6}{5}\binom{5}{5}=$$ $$=1+30+150+200+75+6=462$$