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.

The number of $k$-element subsets of an $n$-element set equals the binomial coefficient $\binom nk$, by definition of that coefficient. Its value can be computed either additively by Pascal's recursion, or by the multiplicative formula
$$
\binom nk=\frac{n(n-1)(n-2)\ldots(n-k+1)}{k!}.
$$
