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?
~~~~~~~~~~~~~~~~~~~~~~


<pre>
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.    <U>ANSWER</U>
</pre>

Solved.