Prove that the product of 
consecutive positive integers divides 
.
Solution
The number of different combinations of 
over 
is of course an integer and equals to
over is of course an integer and equals to
![\[\begin{pmatrix} N+n\\ N \end{pmatrix} = \frac{(N+1)(N+2)...(N+n)}{n!}\]](https://www.math.tolaso.com.gr/wp-content/ql-cache/quicklatex.com-8fa2644b274a0bc0eb3c94a3dfe8daae_l3.png "Rendered by QuickLaTeX.com")
and the result follows.
Any questions?