Counting subsets of a given set Could anyone be kind in helping me with this simple question?
What is the number of subsets of $$\{1,2,3,\cdots, n\}$$ containing k elements?
Thanks.

It is the sum of number of ways of choosing $r$ elements from n elements, where $r$ ranges from $0$ to $n$. This is because $r = 0$ is the null set, $k = 1$ is all $nC1$ subsets of cardinality $1$, and so on...
Just imagine yourself picking all subsets of size 0, then size 1, ..., till size n.
This is also the sum of the nth row of Pascal's Triangle, which is also $2^n$.
Permutations do not count, because the order of a set does not matter.
