Originally Posted by

**mfetch22** How would one go about proving that:

$\displaystyle { n \choose k }$

is always a natural number? That is, assuming $\displaystyle 0 \leq k \leq n$ and that $\displaystyle n = 1, 2, 3, 4...$ and that $\displaystyle k = 1, 2, 3, 4...$; what I mean by that is that $\displaystyle n$ and $\displaystyle k$ are both positive integers. Its a question in my textbook that I bought early to get ahead on fall classes, so I don't have any teachers to ask about this question; not till fall atleast. I'm not asking for a straight out proof, but preferably some direction as to where I would go, which direction I should go to prove this? A litttle guidence is all I need, please don't simply give me the full answer, if you don't mind. Thanks in advance