Question 1207625
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3 empty boxes....<br>
The 8 balls must be distributed to 2 boxes.  The number of ways of choosing 2 of the 5 boxes is C(5,2) = 10.  Using stars and bars (which I will assume you are familiar with, since you are working this kind of problem), the number of ways to distribute the 8 balls in 2 boxes is C(9,1) = 9.<br>
Number of ways to distribute the balls if 3 boxes are empty: 10*9 = 90<br>
4 empty boxes....<br>
The 8 balls must be "distributed" to a single box.  There are 5 boxes to choose from; and for each box chosen there is only one way to put the 8 balls in that box.<br>
Number of ways to distribute the balls if 4 boxes are empty: 5*1 = 1<br>
ANSWER: 90+5 = 95<br>