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We put 12 different balls to 4 equal boxes. How many configurations are possible?

If the boxes were distinguishable it would be simply $4^{12}$, but I do not know how to consider the fact that they are distinguishable.

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When the balls are indistinguishable, you will have the following formula:

\begin{equation} {n+k-1 \choose n} \end{equation}

The formula counts the number of ways in which n indistinguishable balls can be distributed into k distinguishable boxes. In the following link, you can find a good explanation of the reasoning behind it. Number of ways of distributing balls into boxes

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    $\begingroup$ Thank you. But here the balls are distinguishable and the boxes are not. $\endgroup$
    – Uhans
    Feb 10, 2020 at 16:09

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