SOLUTION: 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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Question 1205467: In how many ways can you distribute $8$ indistinguishable balls among $2$ distinguishable boxes, if at least one of the boxes must be empty?
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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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?
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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.    ANSWER

Solved.