+60 In how many ways can you distribute $8$ indistinguishable balls among $2$ distinguishable boxes, if at least one of the boxes must be empty?
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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?
If all eight balls have to be used, and one of the two boxes has to remain empty,
then you have to put all eight balls into the other box. Only two ways to do that.
Either put the balls in box A and leave box B empty, or vice versa.
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+1314
The Edit button to my above has disappeared, so I add the following:
I am accustomed to the occasional ambiguously worded problem, but
this time it must be questioned. Exactly what is meant by “at least one
of the boxes must be empty”? Is it possible for both boxes to be empty?
If both boxes are empty, the solution would contradict itself, because, in
such a case, the balls would not have been distributed.
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