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Five balls, each of a distinct colour, are to be distributed among three boxes of different sizes. Every box is large enough to contain all five balls. In how many ways can the balls be placed into the boxes, if the arrangement of balls inside a box does not matter and no box is left empty?
- 100
- 75
- 150
- 200
Correct answer: 150
Solution
Distributing 5 distinct balls into 3 distinct boxes with none empty counts surjective functions: by inclusion-exclusion 3^5 - C(3,1)*2^5 + C(3,2)*1^5 = 243 - 96 + 3 = 150.
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