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).
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