How does the mathematical form of nCr ensure that the result is a whole number The mathematical form for nCr is
(n!)/(r!(n-r)!)
How does this form ensure that nCr is indeed a whole number. Is there a mathematical proof?

The nice thing is that it is the combinatorial argument that $\frac{n!}{r!(n-r)!}$ counts something (i.e., the number of ways to choose $r$ items from $n$ unordered items) that proves (in the most rigorous sense) that it is a natural number. What are proof is needed?
