# Prove that nCk is a natural number

1. Oct 24, 2009

### nietzsche

1. The problem statement, all variables and given/known data

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 $$1, ..., n$$.

2. Relevant equations

3. 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.

2. Oct 24, 2009

### 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.