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As the title suggests, In how many ways can 20 identical balls be distributed in 3 identical boxes with at most 8 balls in each box and minimum 1 ball in each box ?

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  • $\begingroup$ Number of distributions with minimum $1$ ball-Number of distributions with at least $9$ balls in 1 at least 1 box $\endgroup$ – Qwerty Jun 23 '16 at 16:05
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Well, there's not much leeway, so it's probably most efficient to count by hand: $8+8+4=20$, $8+7+5=20$, $8+6+6=20$, $7+7+6=20$ – that's it, $4$ ways.

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