How many subsets of the set $\{1,2,3,4,5\}$ contain the number 5?
I know that the number of subsets of a set with n elements is $2^n$, since for each element I can choose whether to include it or not in the subset. But this problem asks for a specific condition: the subset must contain 5. That means that I don't have a choice for 5, it has to be in the subset. So the only choices I have are for the other four elements: 1, 2, 3, and 4. For each of them, I can choose to include it or not, so there are $2^4$ ways to do that. Therefore, the number of subsets of the given set that contain 5 is $2^4 = 16$. 