Distributing objects into different boxes such that number of objects are distinct.

Asked Oct 28 '18 at 06:35

Active Oct 28 '18 at 11:26

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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.

edited Oct 28 '18 at 11:26

asked Oct 28 '18 at 06:35

Sahil Silare

What is $x_i{}$? – Angina Seng Oct 28 '18 at 06:37
$x_{i}$ is a positive integer. – Sahil Silare Oct 28 '18 at 06:38
What is $x_i$ in the context of this problem? – Angina Seng Oct 28 '18 at 06:39
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. – N. F. Taussig Oct 28 '18 at 09:13
@N.F.Taussig Please have a look. – Sahil Silare Oct 28 '18 at 11:27
What you are looking for is the number of partitions of $n$ with $t$ distinct parts. The solution is found here. – Jens Oct 28 '18 at 13:13

Distributing objects into different boxes such that number of objects are distinct.

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