Are these the correct equations for the set of following distribution questions?

1. distributing identical balls into a set of distinct boxes empty allowed:

n = number of distinct boxes, m = number of identical balls

$\binom{n+m-1}{m}$ so 5 balls, 3 boxes would result in $\binom{7}{5}$

1. distributing identical balls into a set of distinct boxes with no empty boxes

$\binom{m-1}{n-1}$

1. set of distinct balls into a set of distinct boxes

T(m,n)

• What is T(m,n) ? If it means $n^m$, all ok. – true blue anil Feb 1 '17 at 18:44
• If ball ordering inside each box does not matter – G Cab Feb 1 '17 at 21:44