This question appeared as an unsolved exercise in an introductory combinatorics textbook:
We have a bag with as many identical balls as necessary. We take out i balls and put them in 10 numbered boxes, such that the number of balls in box 1 $\leq $ the balls in box 2 $\leq $ ... $\leq $ the number of balls in box 10 $\leq $ 20. How many ways are there to do this?
A hint is provided (sorry for the shoddy translation): "Think of the sum of the series of differences of the amount of balls in adjacent boxes. The first difference equals the amount of balls in box 1".
Background: Earlier today I asked this question: Number of integer solutions if $x_1\leq x_2\leq x_3\leq ...\leq x_r\leq k$. The question itself was based on this exercise, so I was quite baffled to receive relatively complex answers. I figured I'll ask the question as it appeared, to see if maybe my 'generalisation' made this more complex than it should've been by omitting details.
Thank you for your help as always.