Knapsack problem with the restriction on the number of items
Iterative solution (recursive is very similar too):

Have a 2d array $mat[W][k]$ and let the columns be $0..k$ and the rows be from $0..W$. Let $mat[x][y] = 0 \;\forall \;0\le x \le W, 0\le y \le k$. Let $mat[0][0] = 1$.

Now run $i$ across $[1,k]$. Within the $i$ loop run another loop iterating $j$ across $[1,W]$. In every iteration of the inner loop, run through the set of elements and calculate this:

$${mat[i][j] = \sum_{l=1}^{|X|} mat[i-1][j-X_l] }\:$$

$mat[W][k]$ will store the final answer. Time complexity = $\mathcal{O}(W.k.|X|)$, and space complexity = $\mathcal{O}(W.k)$.