In how many ways I can distribute $n$ objects in $t$ boxes, $x_i$ objects in each box, such that $\sum_i x_{i}=n$ and $x_{i}\neq x_{j}$?

I've taken the case of 5 objects with 2 boxes. Firstly, I filled both boxes with the same elements (1,1) or (2,2) then I filled the remaining ones as (0,3) and (0,1) respectively so that the cases are (1,4) and (2,3) but I am not able to generalize the condition.

  • $\begingroup$ What is $x_i{}$? $\endgroup$ – Lord Shark the Unknown Oct 28 '18 at 6:37
  • $\begingroup$ $x_{i}$ is a positive integer. $\endgroup$ – Sahil Silare Oct 28 '18 at 6:38
  • $\begingroup$ What is $x_i$ in the context of this problem? $\endgroup$ – Lord Shark the Unknown Oct 28 '18 at 6:39
  • $\begingroup$ It does not make sense to say $x_i$ objects in each box if you want a different number of objects in each box. It would be better to say $x_i$ objects in the $i$th box, where $x_i \neq x_j$ for each $i, j$ satisfying $1 \leq i, j \leq t$. You should also edit your question to show what you have attempted and explain where you are stuck so that you receive responses that address the specific difficulties you are encountering. $\endgroup$ – N. F. Taussig Oct 28 '18 at 9:13
  • $\begingroup$ @N.F.Taussig Please have a look. $\endgroup$ – Sahil Silare Oct 28 '18 at 11:27

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