when we apply this formula n+r-1Cr-1

This formula is applied when we have to find the number of non negative integral solutions of the equation, This equation is represented as
x1+x2+x3....+xr = n
Where r is the number of variables and n is the sum of all these variables.
This equation can also be applied in permutations and combinations when we have tp find the number of ways of distributing n identical things into r different boxes.