How many subsets of $\{1,2,3,\ldots,100\}$ contain all the even numbers?
"Contain all the even numbers" means exactly that. Example: $\{2,4,6,...,100,1\}$ contains all the even numbers and $1$.
"Contain all the even numbers" means exactly that. Example: $\{2,4,6,...,100,1\}$ contains all the even numbers and $1$.