Question 68
Let $S = \{1, 2, 3, \dots, 2n\}$, where $n$ is a positive integer greater than or equal to $1$. For any subset $T$ of $S$, $T$ is called a *good* subset if in $T$ the number of even elements is greater than the number of odd elements.
a. Find the total number of good subsets of $S$.
b. Find the sum of all the elements in all the good subsets of $S$.
a. Find the total number of good subsets of $S$.
b. Find the sum of all the elements in all the good subsets of $S$.