Solving 3.1 I think the solution is binomial(n1+r-1,r-1) where n1=n-r, but I obtained that formula by calculating the formula for r=1, then r=2, and the relatio

Solving 3.1 I think the solution is binomial(n1+r-1,r-1) where n1=n-r, but I obtained that formula by calculating the formula for r=1, then r=2, and the relation f(r,n) = sum(f(r-1,n-i),i,0,n) and using maxima with simpsum and factor to obtain a simplified expression whose form suggest the general rule, but I don't see a simpler way.