Question

(n+r-1)c(r-1) formula derivation

Answer 1

with respect to which?

Answer 2

Consider that the number of identical objects is n. Now consider that all these n objects are placed in a row. Let us assume some separators that separates the n objects. Now as we want to separate them into r group [as blank groups are also allowed], take the separators as objects. Now we need r-1 separators to make r groups. Therefore total number of objects is n+r-1. There will be r-1 places for the separators to occupy. Therefore we can arrange the separators in (n+r-1) C (r-1) ways, which is the answer to the question asked.