Balls and Boxes gone crazy. Part-V
Probability
Level
3
Five balls are to be places in three boxes. Each can hold all the five balls. In how many different ways can we place the balls so that no box remains empty, if balls as well as boxes are identical but boxes are kept in a row ?
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The answer is 6.
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Since we need that no box remains empty, we put one ball in each box. We remain with two balls. Now we have 3 ways to put the remaining balls in only one box and 3 ways to put the balls in all but one box. So the answer is 3 + 3 = 6 . Note: since the boxes are put in a row we can consider that the boxes are in fact different one from another.