(a) Given positive integers m, n with m, n, show that the number of ways to distribute...

Question:

(a) Given positive integers m, n with m, n, show that the number of ways to distribute m identical objects into n distinct containers with no container left empty is
C(m - 1, m - n) = C(m - 1, n - 1).
(b) Show that the number of distributions in part (a) where each container holds at least r objects (m > nr) is
C(m - 1 + (1 - r)n, n - 1).