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  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)

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    What is T(m,n) ? If it means $n^m$, all ok. – 2017-02-01
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    If ball ordering inside each box does not matter – 2017-02-01

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