Prove that nCk is a natural number

[nietzsche]

Homework Statement

Prove that \binom{n}{k} is a natural number by showing that \binom{n}{k} is the number of sets of exactly k integers each chosen from 1, ..., n.

Homework Equations

The Attempt at a Solution

I posted a similar question before (https://www.physicsforums.com/showthread.php?t=339363) which asked for a proof by induction. This question is a bit different, and I'm not entirely sure how to get started. I'd appreciate some hints. Thanks.

 

[Dick]

Here's your hint. How many different sequences (ordered!) of integers can you pick from the set {1,...,n}? Count sequences. Mull over that for a bit.