I have a box which contains $n$ unused items (all items in the box are unused). From them I randomly pick $k$, where $k < n$ items. Those $k$ items became used when I picked them, and then I put them back into the box. How to find the probability that second time all $k$ items I pick are going to be unused?(not those which I already picked before)
I already know that all possible ways of picking $k$ from $n$ is: $$\frac{n!}{k!(n-k)!}$$ and that possible ways of picking $k$ from $(n-k)$ is : $$\frac{(n-k)!}{k!((n-k)-k)!}$$