Ways to dispose two numbers in $n>2$ places, when the order is irrelevant

Question

Suppose I have a box containing two numbers, $\{1,0\}$. How do we compute the number of all possible ways to dispose these two numbers in $n>2$ places, when the order is irrelevant?

For example, when $n=2$, we have three possibilities: $(1,1), (1,0), (0,0)$.

Answer 1

This seems to be asking for the number of ways to pick $n$ elements from the set of two with repetition and without order. The answer is actually just $n+1$: you pick $k$ zeros, whers $0\le k\le n$, and then the other elements are forced to be ones.