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  4. The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

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Q. The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is

JEE AdvancedJEE Advanced 2012

Solution:

Number of ways
$=3^{5}-{ }^{3} C_{1} \cdot 2^{5}+{ }^{3} C_{2} 1^{5} $
$=243-96+3=150$