Question: how to prove that $m!$ divides product of $m$ consecutive number .

in other hand :

if we have :$k+1,...,k+m$ then $m! | (k+1)...(k+m)$ $(k,m \in \Bbb Z)$

Answer: 
**Hint:**

Consider the [binomial coefficient](http://en.wikipedia.org/wiki/Binomial_coefficient) $\binom{k+m}{m}$.

Good luck!
Hint: The number $\displaystyle \frac{(k+1)\cdots(k+m)}{m!}$ counts something :)