### Instruction: What is $\dbinom{n}{0}$ for any positive integer $n$?### Response: I know that $\dbinom{n}{k}$ is the number of ways to choose $k$ objects out of $n$ distinct objects, without regard to order.
So, $\dbinom{n}{0}$ is the number of ways to choose $0$ objects out of $n$ distinct objects.
That means I don't choose any of the objects, I just leave them all behind.