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Five balls of different color are to be ...

Five balls of different color are to be placed in three boxes of different size. Each box can hold all five. In how many different ways can we placed the balls so that no box remains empty?

Text Solution

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The correct Answer is:
300
Since, each box can hold five balls. `therefore` Number of ways in which balls could be distributed so that none is empty, are (2, 2, 1) or (3, 1, 1),
i.e. `(""^(5)C_(2) ""^(3)C_(2) ""^(1)C_(1) + ""^(5)C_(3) ""^(2)C_(1) ""^(1)C_(1)) xx 3!`
`= (30 + 20) xx 6 = 300`
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