Hello,

The method I'll present may look a tad weird, and experimental, so don't hesitate if you have any objection lol.

You basically need the two theorems in there : Stars and bars (probability) - Wikipedia, the free encyclopedia

First let a positive integer and a nonnegative integer

For question 1), write the inequality as (think on your own to know why it's correct) and apply theorem 1 (because we have strict inequalities for the unknowns).

For question 2), we have

Let and

Substitute the by the in the inequality to get :

, where

and you can apply theorem 2.