Division of Factorials [binomal coefficients are integers] I have a partition of a positive integer $(p)$. How can I prove that the factorial of $p$ can always be divided by the product of the factorials of the parts?
As a quick example $\frac{9!}{(2!3!4!)} = 1260$ (no remainder), where $9=2+3+4$.
I can nearly see it by looking at factors, but I can't see a way to guarantee it.

If you believe (:-) in the two-part Newton case, then the rest is easily obtained by induction. For instance (to motivate you to write a full proof):
$$\frac{9!}{2! \cdot 3! \cdot 4!}\ =\ \frac{9!}{5!\cdot 4!}\cdot \frac{5!}{2!\cdot 3!}$$
