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In how many ways can you distribute $8$ indistinguishable balls among $2$ distinguishable boxes, if at least one of the boxes must be empty?

 Dec 24, 2023
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Let the boxes be B1 and B2.


It it obvious, that under given condition, EITHER box B1 OR box B2 must be empty.

 

If box B1 is empty, then all 8 indistinguishable balls are in box B2: so, there is only one such distribution.

 

If box B2 is empty, then all 8 indistinguishable balls are in box B1: so, there is only one such distribution.

 

In all, there are 1 + 1 = 2 such distinguishable distributions.

 Dec 25, 2023

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