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JEE Main Mathematics question

MathematicsPermutations and CombinationsJEE Main

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

Answer: (C)

Solution

Each ball goes into one of different boxes, and no box may stay empty, so we count onto maps from balls to boxes. By inclusion-exclusion the count is

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Question ID VK-020694