How many ways are there of choosing $k$ distinct items from a set of $n$? Specifically, say I have the integers $1,2,3,\dots,n$ (a set of $n$ integers). I want to select numbers one after another (not at the same time) until I have $k$ distinct numbers. How many ways are there of doing this? Someone told me $nPk$ but I don't understand why. Is there another way to approach it?

http://en.wikipedia.org/wiki/Binomial_coefficient
Please, someone change tag to combinatorics. Additive combinatorics is not about that.
